This question is from NCERT Book class 10th Ch. no.5 Ex. 5.1 Q. 10 (x). 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 yes then find the common difference and the next three terms. a, 2a, 3a, 4a ….

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Solution:a, 2a, 3a, 4a…The difference of the above series is:-

a_{2}–a_{1}= 2a–a=aa_{3}–a_{2}= 3a-2a=aa_{4}–a_{3}= 4a-3a=aHere, common difference is same every time.

Hence, d =

aand the given series forms a A.P.So, The three terms are;

a_{5}= 4a+a= 5aa_{6}= 5a+a= 6aa_{7}= 6a+a= 7a