Question

The first and last term of an A.P. are a andl respectively. If s be the sum of all terms of the A.P., then the common difference is –

• A. $\frac{l^{2} - a^{2}}{2s - (l + a)}$
• B. $\frac{l^{2} - a^{2}}{2s - (l - a)}$ f
• C. $\frac{l^{2} + a^{2}}{2s + (l + a)}$
• D. $\frac{l^{2} + a^{2}}{2s - (l + a)}$

Answer 1

Answer: (A)

$\frac{l^{2} - a^{2}}{2s - (l + a)}$

Answer 2

l = a + (n – 1) d ̃ n = $\frac{l - a + d}{d}$

Now S = $\frac{n}{2}$ (a + l)

̃ S = $\frac{l - a + d}{2d}$ (a + l)

d =$\frac{l^{2} - a^{2}}{2s - (a + 1)}$.