The first term of an AP is – 5 and the last term is 45. If the sum of the terms of the AP is 120, then find the number of terms and the common difference.

Let the first term, common difference and the number of terms of an AP are a, d and n respectively.

Given that, first term, a = - 5

last term, a_n = 45

Sum of the terms of the AP , S_n = 120

We know that, if last term of an AP is known, then sum of n terms of an AP is,

240 = 40n

n = 6

Also we know the nth term formula

a_n = a + (n - 1)d

45 = - 5 + (6 - 1)d

50 = 5d

d = 10

Hence, number of terms and the common difference of an AP are 6 and 10 respectively.