Question

The sum of n terms of three A.P.'s whose first term is 1 and

common differences are 1, 2, 3 are $S_1$, $S_2$, $S_3$ respectively. The true

relation is

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

We have $a_1$ = $a_2$ = $a_3$ = 1 and $d_1$ = 1, $d_2$ = 2, $d_3$ = 3.

Therefore, $S_1$ = $\frac{n}{2}$(n + 1) ..........(i)

$S_2$ = $\frac{n}{2}$[2n] ...........(ii)

$S_3$ = $\frac{n}{2}$[3n - 1] ...........(iii)

Addding (i) and (iii),

$S_1$ + $S_3$ = $\frac{n}{2}$[(n + 1) + (3n - 1)] = 2[$\frac{n}{2}$(2n)] = 2$S_2$

Hence correct relation $S_1$ + $S_3$ = 2 $S_2$.