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  • Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. (x) a, 2a, 3a, 4a, ...

Q : 4       Which of the following are APs ? If they form an AP, find the common difference d and write three more terms.

                (x)   \small a,2a,3a,4a,...

Answers (1)

best_answer

Given series is
\small a,2a,3a,4a,...
Now,
first term to this series is = a
Now,
a_1 = a \ \ and \ \ a_2 = 2a \ \ and \ \ a_3 = 3a \ \ and \ \ a_4 = 4a
a_2-a_1 = 2a-a =a
a_3-a_2 = 3a-2a =a
a_4-a_3=4a-3a=a
We can clearly see that difference between terms are equal  and equal to a
Hence, given series is in AP
Now, next three terms are
a_5=a_4+d =4a+a=5a
a_6=a_5+d =5a+a=6a
a_7=a_6+d =6a+a=7a
Therefore, next three terms of given series are  5a,6a,7a

Posted by

Gautam harsolia

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