Question

the sum of the 5th & 9th termsof a A.P is 136 & that of first 15 terms is 465 .then find the sum of the first 25 terms.​

Answer 1

Answer:

- 3580 is the sum of first 25 terms

Step-by-step explanation:

5th term = a + 4d

9th term = a + 8d

5th term + 9th term = 136

a + 4d + a + 8d = 136

2a + 12d = 136

2(a + 6d) = 136

a + 6d = 136/2 = 68 equ (1)

sum of first 15 terms = 465

$465 = \frac{15}{2} (2a + 14d) \\ 465 = \frac{15}{2} \times 2(a + 7d) \\ \frac{465}{15} = a + 7d \\ a + 7d = 31 \: \: \: \: \: equ \: (2)$

subtract (2) - (1)

d = - 37

substitute d = -37 in equ (1)

a + 6d = 68

a + 6(-37) = 68

a - 222 = 68

a = 68 + 222

a = 290

sum of first 25 terms

$= \frac{25}{2} (2(290) + 24( - 37) \\ = \frac{25}{2} (580 - 888) \\ = \frac{25}{2} \times - 308 \\ = 25 \times - 154 \\ = - 3580$

hope you get your answer