Question

If 5 times an arthemetic sequence is equal to its 5th term and 8times is equal to its 8th term what is the sum of first 25 terms

Answer 1

Answer:

Let a be the first term and d be their common difference of the AP.

Then, nth term of the AP T

n

=a+(n−1)d

Given, 8×T

8

=12×T

12

=>8(a+(8−1)d)=12(a+(12−1)d)

=>8(a+7d)=12(a+11d)

=>2(a+7d)=3(a+11d)

=>2a+14d=3a+33d

=>a=−19d

So, T

20

=a+(20−1)d=−19d+19d