Question

In an A.P. if $S_n=2n^2+3n$ ; then $t_{20}$ =

Answer 1

Given that $S_n=2n^2+3n$

$S_1=2(1{)}^2+3(1)=2+3=5$

So, sum of the first term of A.P. is $5$

$⟹$ first term $a=5$

$S_2=2(2{)}^2+3(2)=8+6=14$

So, sum of the first two terms of A.P. is $14$

$⟹$ first term +second term $=14$

$⟹5+a_2=14$

$⟹a_2=9$

Therefore, $\text{common difference = second term - first term}$

$⟹d=14-5=9$

Therefore, $t_{20}=a+(20-1)d$

$⟹t_{20}=5+\left(19\right)9$

$⟹t_{20}=5+171=176$