Question

E sum of 5 terms of an ap is 50 and that of next 3 is 66. find the ap

Answer 1

According to given condition, S5 = 25

⇒ 2a + 4d = 10  ........ (1)

Given, S1+ S2 +  .......  + S5 = 25 and

S6 + S7 +  .......  + S10 = –75

⇒ S1 + S2 +  .......  + S9 + S10  = 25 –75 = –50

⇒ S10 = – 50

5 [ 2a + 9d] = – 50

2a + 9d = – 10  .........(2)

Subtract (1) from (2), we get

2a + 9d –2a – 4d = – 10 – 10

5d = – 20

⇒d = – 4

On putting value of d in (1), we get

2a + 4(–4) = 10

2a – 16 = 10

2a = 26

⇒ a = 13

∴ 10th term of A.P. = a10 = a + 9d

= 13 + 9 (– 4)

= – 23