Question

The sum of 15 terms of an A.P. is zero. Its 4th term is 12. Find its 14th 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 + (4 − 1)d

a + 3d = 12

−7d + 3d = 12

−4d = 12

d = `12/-4`

d = −3

a = −7d

= (−7) × (−3)

= 21

a₁₄ = a + (14 − 1)d

= 21 + 13 × (−3)

= 21 − 39

= −18