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How to find whether a sequence of numbers are in Arithmetic Progression or not?

Asked by Avinash Bikumalla Last Modified

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58 Answers 16 Likes | 5 DisLikes

Take any three consecutive terms, if the twice of middle term is equal to the sum of remaining two then series is in A.P.

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Comments If the difference between all the consecutive terms is same then they are in AP. For ex 3,7,11,15,19..... Here difference (7-3) =(11-7) =(15-11) and so on.. between all the consecutive terms is 4. So they are in AP.

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Comments To check whether the numbers are in AP or not, first calculate the difference between every two consecutive term i.e. 2nd term - 1st term, 3rd term - 2nd term, 4th term - 3rd term and so on. If the difference is same in every case then the numbers are in AP and the same difference obtained in every case is common difference.

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POST YOUR REQUIREMENT NOWA series in which the difference is common everywhere in known as A. P. So u just have to check whether the difference is common or not. The difference should be seen between every term nd the one preceeding it.

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Comments Rajesh Chaudhary

I am a graduate(B.Tech) from National Institute of Technology Karnataka with a degree in Information Technology and am also able to teach Maths and Computer to 'A' level.

A sequence of numbers are in A.P. if this sequence has the property that the difference between successive terms is constant. for ex- a,b,c is a sequence of number then deference d1=b-a, d2=c-b now a,b,c will be in A.P. if and only if d1=d2

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Comments second term-first term=third - second term then the sequence is said to be in arithmetic progression.

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Comments A.p can be written as a,a+d,a+2d,.. a+(n-1)d Here a is ur 1st term and d is common difference =2nd term-1st term or 3rd term - 2nd term and so on.... let u explain by example.let the sequence is 1,3,5,7,9,.... Ans since 2nd term -1st term=3rd term - 2nd term=4th term - 3rd term = 2 (common diff (d)),so the sequence1,3,5,7,..are in a.p..and if the common difference is not same then the sequence is not an a.p...

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Comments To find wether a no is an AP or not u have to look for the common diffrence . Let there be three terma a1,a2,a3 then if a3-a2 =a2-a1 and so on for all the terms then sequence is an AP . For eg 2,4,6,8,10 in this we have a common difernce i.e 2 so its an ap 2,4,8,16 Here the diference between adjacent term is not same and hence its not an AP 10,8,6,4,2 it has same difence of -2 and hence this is also an AP Tip: try subtracting any adjacent terms and check weather they have same differmce bw them

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Comments Koushik Ganguly

Private tuition for science and maths

subtract 1st term from the 2nd term of the sequence, and obtain the common difference,similarly find C.D for the other twrms, if they are equal then it is in A.P

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