Question

If 5th and 15th term of ap are 13 and -17 find sum of 21 terms

Answer 1

Answer:

a5=13, a15=-17

a+4d=13 1.

a+14d=-17 2.

Subtract equation 1. from 2.

a + 14d = -17

a + 4d = 13

(-) (-) (-)

10d = -30

d = -30/10

d = -3

Put the value of d in eq. 1.

a + 4d = 13

a + 4×-3 = 13

a - 12 = 13

a = 13+ 12

a = 25

Sn = n/2 [2a + (n-1) d]

S21= 21/2 [2×25 + (21-1) ×-3]

S21= 21/2 (50 + 20 × -3)

S21= 21/2 (50 -60)

S21= 21/2 ×-10

S21= 21 ×-5

S21= -105