Question

The sum of first ${}^{\prime }{n}^{\prime }$ terms of an Arithmetic Progression is $"5n^2-2n"$. Find the ${20}^{th}$ term?

• A. $1960$
• B. $183$
• C. $203$
• D. $193$

Answer 1

The correct option is D $193$

Sum of first n terms of AP$=5n^2-2n$
Let first term$=a$ and
difference $=d$
So, $\frac{n}{2}(2a+(n-1)d)=5n^2-2n$
$2an+n^{2}d-nd=10n^2-4n$
$n^{2}d-n(d-2a)=10n^2-4n$
Comparing co efficients
$d=10$
$d-2a=4$
$10-2a=4$
$a=3$
So, ${20}^{th}$ term
$a+(n-1)d$
$=3+(20-1)10$
$=3+190=193$