Question

The sum of 15 terms of an A.P. is zero, and its 5th term is 12. Find its 12th term.

Answer 1

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

`S_15 = 15/2[2a + (15 - 1)d]`

2a + 14d = 0

2a = −14d

a = `(−14d)/2`

a = −7d

a_n = a + (n − 1)d

a_n = a + (5 − 1)d

a + 4d = 12

−7d + 4d = 12

−3d = 12

d = `12/-3`

d = −4

a = −7d

a = (−7) × (−4)

a = 28

a₁₂ = a + (n − 1)d

= 28 + (12 − 1)(−4)

= 28 + 11 × (−4)

= 28 − 44

= −16