Question

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.

Answer 1

Given that, \(a = 5\), \(l = 45\) and \(S_n = 400\)
\(S_n = \frac n2(a+l)\)

\(400 = \frac n2(5+45)\)

\(400 = \frac n2(50)\)

\(\frac { 400 \times 2}{50} = n\)

\(n = 16\)
\(l = a + (n−1)d\)
\(45 = 5 + (16 − 1) d\)
\(40 = 15d\)

\(d = \frac {40}{15}\)

\(d = \frac {8}{3}\)