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

Sum of first 25 terms = Sum of next 15 terms => (T_1 + T_2 + * s + T_25) = (T_26 + T_27 + * s + T_40) => (T_1 + T_2 + * s + T_40) = 2(T_1 + T_2 + * s + T_25) (40 / 2) [2a + 39d] = 2 x (25 / 2) [2a + 24d] 20(2a + 39d) = 25(2a + 24d) 40a + 780d = 50a + 600d 180d = 10a d = (a / 18) Given a = 3, => d = (1 / 6)

If the first term of an A.P. is 3 and the sum of its fi... | Sequence & Series (Mathematics)

Sum of first 25 terms = Sum of next 15 terms

\Rightarrow (T_1 + T_2 + \cdots + T_{25}) = (T_{26} + T_{27} + \cdots + T_{40})

\Rightarrow (T_1 + T_2 + \cdots + T_{40}) = 2(T_1 + T_2 + \cdots + T_{25})

\frac{40}{2}\,[2a + 39d] = 2 \times \frac{25}{2}\,[2a + 24d]

20(2a + 39d) = 25(2a + 24d)

40a + 780d = 50a + 600d

180d = 10a

d = \frac{a}{18}

\text{Given } a = 3,\ \Rightarrow\ d = \frac{1}{6}

Explanation

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