Class 11

Math

Algebra

Sequences and series

The second and the last term of an A.P. are $18$ and $720$ respectively and their common difference is $6$. What is their sum?

- $S_{n}=48,665$
- $S_{n}=43,554$
- $S_{n}=43,665$
- $S_{n}=42,665$

$d=a_{2}−a_{1}$

$6=18−a_{1}$

$a_{1}=12$

We know that, last term, $l=a+(n−1)d$

$⇒720=12+(n−1)6$

$⇒720=12+6n−6$

$⇒720−6=6n$

$⇒n=6714 $

$⇒n=119$

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

$=2119 [12+720]$

$=59.5[732]$

Therefore, $S_{n}=43,554$