Question

The first and the last term of A.P. are $7$ and $630$ respectively. If the common difference is $7$, how many terms are there and what is their sum?

• A. $S_n=28,665;n=90$
• B. $S_n=28,665;n=91$
• C. $S_n=28,665;n=92$
• D. $S_n=28,665;n=95$

Answer 1

The correct option is A $S_n=28,665;n=90$

Given that, $a_1=7;$ last term $=l=630,d=7$
We know that, last term, $1=a+(n-1)d$
$\Rightarrow 630=7+(n-1)7$
$\Rightarrow 630=7+7n-7$
$\Rightarrow \frac{630}{7}=n$
$\Rightarrow n=90$
We know $S_n=\frac{n}{2}$ [First term $+$ Last term]
$=\frac{90}{2}[7+630]$
$=45\left[637\right]$
Thus $S_n=28,665$