The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

Here, a = 5, a_n = 45 and S_n = 400.
The sum of n terms of an AP is given by
S_n = n/2[a + a_n]
⇒ 400 = n/2[5 + 45]
⇒ 400 = 25n
⇒ n = 400/25 = 16
a_n = a + (n – 1)d
⇒ 45 = 5 + (16 – 1)d
⇒ 40 = 15d
⇒ d = 40/15 = 8/3
Hence, the number of term are 16 and the common difference is 8/3.