Class 11

Math

Algebra

Sequences and Series

The sum of first $n$ terms of $A.P.$ is $5n−2n_{2}$. Find the $A.P.$ i.e., $a$ and $d$.

$S_{n}=5n−2n_{2}$

First term, $a_{1}=S_{1}=5(1)−2(1)_{2}=3$

Sum of first two terms ,$S_{2}=5(2)−2(2)_{2}=2$

Second term ,$a_{2}=S_{2}−S_{1}=2−3=−1$

Common difference $d=a_{2}−a_{1}=−1−3=−4$

$a_{n}=a+(n−1)d$

$a_{n}=3+(n−1)(−4)$

$a_{n}=3−4n+4$

$a_{n}=7−4n$

$nth$ term of an A.P$=7−4n$

Therefore A.P is

$3,−1,−5,−9........$

$∴a=3,d=−4$