This question is from NCERT Book class 10th Ch. no.5 Ex. 5.1 Q. 12 (xii). In this question find that the given series is an A.P or not after this find the common difference and the next three terms of the series. find the Solution.

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# In the following question find that the given series is an A.P or not. Then find the C.D and next 3 values of the A.P. √2, √8, √18, √32 …

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Solution:√2, √8, √18, √32 …

The difference between the terms above is:-

a_{2}–a_{1}= √8 – √2 = 2√2 – √2 = √2a_{3}–a_{2}= √18 – √8 = 3√2 – 2√2 = √2a_{4}–a_{3}= 4√2 – 3√2 = √2The common difference is same in each case.

So, the given series forms a A.P.

Now next 3 terms will be:-

a5= √32+√2 = 4√2+√2 = 5√2 = √50a6= 5√2+√2 = 6√2 = √72a7= 6√2+√2 = 7√2 = √98