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 :
JEE · Math · previous-year question
- A.$${1 \over 4}$$
- B.$${1 \over 5}$$
- C.$${1 \over 7}$$
- D.$${1 \over 6}$$correct
Answer
D. $${1 \over 6}$$
Explanation
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 = $${1 \over 6}$$
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