Question

In an A.P, the sum of the first ten terms is 210 and the difference between the first and the last term is 36. Find the first term in the A.P. :

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

Answer: (B)

3

Let $S_n$ denote sum of first $n$ terms.

$\therefore S_n=\frac{n}{2}(a+l)$, where $a$ is the first term and $l$ is the last term.

As given, sum of first ten terms is 210

$⟹S_{10}=\frac{10}{2}(a+l)$

$⟹210=5(a+l)$

$⟹42=a+l$ ............ (1)

And also $l-a=36$ ............ (2)

Solving (1) and (2) simultaneously we get

$l=39$

Substituting $l$ in (2) we get, $a=3$.

Hence, $3$ is the first term.