This question is from NCERT Book class 10th Ch. no.5 Ex. 5.1 Q. 15 (xv). In this question find that the given series is an A.P or not then find the common difference and the next three terms of the series. Give the solution of the above Question.

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# Find that the given series is an A.P or not if it is then find the common difference and the next three values of the given series. 12, 52, 72, 73 …

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1^{2}, 5^{2}, 7^{2}, 73 …Or 1, 25, 49, 73 …

Here,

a_{2}−a_{1}= 25−1 = 24a_{3}−a_{2 }= 49−25 = 24a_{4}−a_{3}= 73−49 = 24The given series forms a Arithmetic Progression because

The common difference is same every case.

So, here the next three values of the given series are:-

a_{5}= 73+24 = 97a_{6}= 97+24 = 121a_{7 }= 121+24 = 145