Question

If the 10th term of an ap is 0 and 42nd term is -32 then nth term is

Answer 1

Given 10th term of A.P = 0
Therefore
a + 9d = 0 (Equation 1)

Also given that the 42nd term = - 32
Therefore
a + 41d = - 32 (Equation 2)

Subtracting equation 2 from 1
a + 9d = 0
- a - 41d = 32

- 32d = 32
d = - 1

a + 9 (-1) = 0
a - 9 = 0
a = 9

Therefore nth term = a + (n - 1)d
                                 = 9 + (n - 1)- 1
                                 = 9 - n + 1
                                 = 10 - n

Therefore option(1) is right.

Hope this helps you.