If the first term of an A.P.

Question

If the first term of an A.P. is $3$ and the sum of its first $25$ terms is equal to the sum of its next $15$ terms, then the common difference of this A.P. is:

Accepted Answer

First 25 terms = a, a + d, .......,a + 24d

Next 15 terms = a + 25d, a + 26d, ......, a + 39d

$$ \therefore $$ $${{25} \over 2}\left[ {2a + 24d} \right] = {{15} \over 2}\left[ {2\left( {a + 25d} \right) + 14d} \right]$$

$$ \Rightarrow $$ 50a + 600d = 15 [2a + 50d + 14d]

$$ \Rightarrow $$ 20a + 600d = 960d

$$ \Rightarrow $$ 60 = 360d

$$ \Rightarrow $$ d = $${1 \over 6}$$

Solutions · 1