Number series :
Number series mathematics ke bahut he important chapter hain.All competitive exam me number series se minimum 5 question puche jate hai unme se 3 question easy hote hai.Bank exam me 5 question and ssc, cpo, mts, aur baki all competitive exam me number series se question ate hain.
Aaj iss post me hum janenge number series ki basics jankari hindi me.Agar app apna number series ke basics concept clear karna chateho to iss post ko dhayan se pura read kare.Kyunki iss post pura padne ki baad apki number series ki basics concept clear ho jayege.
What is number series in math?
Sabse pehle hum janenhe mathematics me number series ki definition kya hote hain.
Maths ke number series me kuch numbers ko left se right me ek particular sequence me arranged kiye jate hai.Isme sabhi numbers same pattern me change hote hai.khabi khabi ek ya usse jada numbers ko series me wrongly put kiye jate hain aur isse pattern ki through hume bho wrong numbers ko find karna hote hai.
Ex1:Find out the missing term of 1,4,...,16.25.36. Iss series me sabhi numbers ko natural numbers ki square me arranged kiye gaye hain.
1^2 = 1, 2^2 = 4, 3^2 = 9, 4^2 = 16, 5^2 = 25, 6^2 = 36.
Therefore missing number is 3^2 = 9.
Ex:2. Find the wrong number of the series 1,4,9,15,25.
Soln: Iss series me bhi all number ko natural numbers ke square me arranged kiye gaye hai.i.e. wrong number is 15.
Different type of number series:
Aise to number series bahut sare type ke hote hai.iss post me hum kuch important type ki bare discuss karenge. jisse sabhi competitive exam me question puche jate hain.
Prime number Series: Iss type of series me sabhi numbers ko prime number ki sequence me arrange kiye jate hai.
For example ,find the next term in the series 2,3,5,7,11,13,....?
Soln: Given series ko consecutive prime numbers me arranged kiye gaya hai .i.e. next term is 17.
Perfect square series:
Iss type of series me sabhi number ko perfect square me arranged kiye jate hain.perfect square series ko n^2 series bhi kaha jate hai.
Ex:- Find out the next terms in the series 1,4,9,16,..?
Soln: 1^2 = 1, 2^2 = 4, 3^2 = 9, 4^2 = 16, 5^2 = 25. i.e. next term = 25.
Ex.2: Find the missing terms in the series 100,121,144,...,196.
Soln: Here 100=10^2, 121 = 11^2, 144 = 12^2, 169 = 13^2, 196 = 14^2, then missing term = 169.
Perfect cube series (n^3):
Perfect cube type of series me all numbers ko perfect cube me arranged kiye jate hain.
Ex1: Find the missing term in the series 1,8,27,....,125.
Soln: 1^3 = 1, 2^3 = 8, 3^3 = 27, 4^3 = 64, 5^3 = 125,therefore missing number is 64.
Ex2: Find out the missing term in the series 1331,....,2197.2744.
Soln: 11^3 = 1331, 12^3 = 1728, 13^3 = 2197, 14^2 = 2744,then missing term = 1728.
Addition series:
Jis type of series me privious term ke sath kuch specific numbers ko add karke next term milte hai.usse addition series kehte hain.addition series ko increasing order series bhi kehte hai.iss series me consecutibe two numbers se difference same hote hain.
Ex1: Find the missing term in the series 2,7,12,17,..., 27.
Soln: 2+5 = 7, 7+5 =12, 12+5 = 17, 17+5= 22, 22+5=27,therefore missing term = 22.
Difference Series:
Difference series decreasing order series hote hain. iss type of series me previous term se fixed or specific number substracting karne ki baad next term milte hain.
Ex.1: Find out the missing term in the series 27,22,17,...,7.
Soln: 27 - 5 = 22, 22 - 5 = 17, 17 - 5 = 12, 12 - 5 = 7.then missing term = 12.
Multiple Series:
Iss type of series me privious term ke sath kuch specific number ko multiple karne ke baad next term milte hai. isme specific number same or cosecutive hogi.
For example, Find the missing term in the series 2,4,8,16,32,...., 128.
Soln: Iss series me privious number ke sath 2 multiple karne se next number milte hai.
2*2 = 4, 4*2 = 8, 8*2 = 16, 16*2 = 32, 32*2 = 64, 64*2 = 132.
Therefore missing number = 64.
Division Series:
Division series me Previous number ke sath kuch specific same or consecutive number se divide karne se next number milte hain.
Ex.1: Find the missing number in the series 512,216,72,....,12.
Iss series me Previous number ko alternately 2 and 3 se divide karne se next number milte hai.
512/2 = 216, 216/3 = 72, 72/2 = 36, 36/ 3 = 12.then the missing number is = 36.
Ratio Series:
Soln: Iss type of series me numbers ko two numbers ki ratio ke hisab se arranged kiye jate hai.
Ex: Find out the next number in the series 336,168,84,42,21,....?
Soln: Iss series me Previous and next number 2:1 ratio me hai. i.e. next number = 10.5 .
Two-tier arithmatic Series:
Two-tier arithmetic series two different series ki combination me hote hain. Iss type of series me two different operations successive terms me performed karte hai.
Ex: Find out the next number in the series 4,5,9,16,26,39,55,...,?
Soln:
Geometric Series:
Geometric series assending or desending order ki uppore based hote hai.Iss type of series me Previous number ke sath kuch specific number multiplying or dividing karne se successive number milte hai.
Ex: 3,6,12,24,48,...,?
Soln: 3*2 = 6, 6*2 = 12, 12*2 = 24, 24*2 = 48, 48*2 = 96.therefore next number = 96.
Mixed Series:
Mixed series me two or more different type of series ko single series me alternately arranged kiye jate hain.
For example, 1,1,4,8,9,27,16,64...?
iss series me perfect square and perfect cube series ko alternately arranged kiye gaye hai.
1.) 1,4,9,16,...... Perfect square series.
2.) 1,8,27,64,...... Perfect cube series.
I hope iss post ko pura padne ke baad aapki number series ki basics concept clear ho gaya hai.Agar number series se related koi question ya suggetion hain to jarur comment karke bataye.Aur iss post ko apna dosto ke sath share jarur kare taki unhe bhi pata chale ki number series kya hai.
Number series mathematics ke bahut he important chapter hain.All competitive exam me number series se minimum 5 question puche jate hai unme se 3 question easy hote hai.Bank exam me 5 question and ssc, cpo, mts, aur baki all competitive exam me number series se question ate hain.
Aaj iss post me hum janenge number series ki basics jankari hindi me.Agar app apna number series ke basics concept clear karna chateho to iss post ko dhayan se pura read kare.Kyunki iss post pura padne ki baad apki number series ki basics concept clear ho jayege.
What is number series in math?
Sabse pehle hum janenhe mathematics me number series ki definition kya hote hain.
Maths ke number series me kuch numbers ko left se right me ek particular sequence me arranged kiye jate hai.Isme sabhi numbers same pattern me change hote hai.khabi khabi ek ya usse jada numbers ko series me wrongly put kiye jate hain aur isse pattern ki through hume bho wrong numbers ko find karna hote hai.
Ex1:Find out the missing term of 1,4,...,16.25.36. Iss series me sabhi numbers ko natural numbers ki square me arranged kiye gaye hain.
1^2 = 1, 2^2 = 4, 3^2 = 9, 4^2 = 16, 5^2 = 25, 6^2 = 36.
Therefore missing number is 3^2 = 9.
Ex:2. Find the wrong number of the series 1,4,9,15,25.
Soln: Iss series me bhi all number ko natural numbers ke square me arranged kiye gaye hai.i.e. wrong number is 15.
Different type of number series:
Aise to number series bahut sare type ke hote hai.iss post me hum kuch important type ki bare discuss karenge. jisse sabhi competitive exam me question puche jate hain.
Prime number Series: Iss type of series me sabhi numbers ko prime number ki sequence me arrange kiye jate hai.
For example ,find the next term in the series 2,3,5,7,11,13,....?
Soln: Given series ko consecutive prime numbers me arranged kiye gaya hai .i.e. next term is 17.
Perfect square series:
Iss type of series me sabhi number ko perfect square me arranged kiye jate hain.perfect square series ko n^2 series bhi kaha jate hai.
Ex:- Find out the next terms in the series 1,4,9,16,..?
Soln: 1^2 = 1, 2^2 = 4, 3^2 = 9, 4^2 = 16, 5^2 = 25. i.e. next term = 25.
Ex.2: Find the missing terms in the series 100,121,144,...,196.
Soln: Here 100=10^2, 121 = 11^2, 144 = 12^2, 169 = 13^2, 196 = 14^2, then missing term = 169.
Perfect cube series (n^3):
Perfect cube type of series me all numbers ko perfect cube me arranged kiye jate hain.
Ex1: Find the missing term in the series 1,8,27,....,125.
Soln: 1^3 = 1, 2^3 = 8, 3^3 = 27, 4^3 = 64, 5^3 = 125,therefore missing number is 64.
Ex2: Find out the missing term in the series 1331,....,2197.2744.
Soln: 11^3 = 1331, 12^3 = 1728, 13^3 = 2197, 14^2 = 2744,then missing term = 1728.
Addition series:
Jis type of series me privious term ke sath kuch specific numbers ko add karke next term milte hai.usse addition series kehte hain.addition series ko increasing order series bhi kehte hai.iss series me consecutibe two numbers se difference same hote hain.
Ex1: Find the missing term in the series 2,7,12,17,..., 27.
Soln: 2+5 = 7, 7+5 =12, 12+5 = 17, 17+5= 22, 22+5=27,therefore missing term = 22.
Difference Series:
Difference series decreasing order series hote hain. iss type of series me previous term se fixed or specific number substracting karne ki baad next term milte hain.
Ex.1: Find out the missing term in the series 27,22,17,...,7.
Soln: 27 - 5 = 22, 22 - 5 = 17, 17 - 5 = 12, 12 - 5 = 7.then missing term = 12.
Multiple Series:
Iss type of series me privious term ke sath kuch specific number ko multiple karne ke baad next term milte hai. isme specific number same or cosecutive hogi.
For example, Find the missing term in the series 2,4,8,16,32,...., 128.
Soln: Iss series me privious number ke sath 2 multiple karne se next number milte hai.
2*2 = 4, 4*2 = 8, 8*2 = 16, 16*2 = 32, 32*2 = 64, 64*2 = 132.
Therefore missing number = 64.
Division Series:
Division series me Previous number ke sath kuch specific same or consecutive number se divide karne se next number milte hain.
Ex.1: Find the missing number in the series 512,216,72,....,12.
Iss series me Previous number ko alternately 2 and 3 se divide karne se next number milte hai.
512/2 = 216, 216/3 = 72, 72/2 = 36, 36/ 3 = 12.then the missing number is = 36.
Ratio Series:
Soln: Iss type of series me numbers ko two numbers ki ratio ke hisab se arranged kiye jate hai.
Ex: Find out the next number in the series 336,168,84,42,21,....?
Soln: Iss series me Previous and next number 2:1 ratio me hai. i.e. next number = 10.5 .
Two-tier arithmatic Series:
Two-tier arithmetic series two different series ki combination me hote hain. Iss type of series me two different operations successive terms me performed karte hai.
Ex: Find out the next number in the series 4,5,9,16,26,39,55,...,?
Soln:
Geometric Series:
Geometric series assending or desending order ki uppore based hote hai.Iss type of series me Previous number ke sath kuch specific number multiplying or dividing karne se successive number milte hai.
Ex: 3,6,12,24,48,...,?
Soln: 3*2 = 6, 6*2 = 12, 12*2 = 24, 24*2 = 48, 48*2 = 96.therefore next number = 96.
Mixed Series:
Mixed series me two or more different type of series ko single series me alternately arranged kiye jate hain.
For example, 1,1,4,8,9,27,16,64...?
iss series me perfect square and perfect cube series ko alternately arranged kiye gaye hai.
1.) 1,4,9,16,...... Perfect square series.
2.) 1,8,27,64,...... Perfect cube series.
I hope iss post ko pura padne ke baad aapki number series ki basics concept clear ho gaya hai.Agar number series se related koi question ya suggetion hain to jarur comment karke bataye.Aur iss post ko apna dosto ke sath share jarur kare taki unhe bhi pata chale ki number series kya hai.
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