Class 11

Math

Algebra

Sequences and Series

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?

- $S_{n}=28,665;n=90$
- $S_{n}=28,665;n=91$
- $S_{n}=28,665;n=92$
- $S_{n}=28,665;n=95$

We know that, last term, $1=a+(n−1)d$

$⇒630=7+(n−1)7$

$⇒630=7+7n−7$

$⇒7630 =n$

$⇒n=90$

We know $S_{n}=2n $ [First term $+$ Last term]

$=290 [7+630]$

$=45[637]$

Thus $S_{n}=28,665$