Question

If the sum of the first 14 terms of an A.P. is 1050 and its first term is 10, find the 20th term.

Hint:

Use the sum formula to find the common difference before solving for any term.

Answer 1

Sum of an A.P:
\[ S_n = \frac{n}{2} [2a + (n-1)d]. \] \[ 1050 = \frac{14}{2} [2(10) + 13d]. \] \[ 1050 = 7 [20 + 13d]. \] \[ 150 = 20 + 13d. \] \[ 13d = 130. \] \[ d = 10. \] Now,
\[ a_{20} = a + (20-1)d = 10 + 19(10) = 200. \]