Question

In an A.P. the sum of '$n$' terms is $5n^2-5n$. Find the 10th term of the A.P.

• A. $80$
• B. $90$
• C. $100$
• D. $110$

Answer 1

Answer: (B)

$90$

Sum of the $n$ terms $=5n^2-5n$

$\because$ $S_n=\frac{n}{2}(2a+(n-1\left)d\right)$, where $a$ is the first term.
$S_1=$ sum of 1 term $=5-5$
$=0$
$\therefore$ $a_1=\mathrm{0.......}\left(1\right)$
$S_2=$ sum of 2 terms $=5{\left(2\right)}^2-5\left(2\right)$
$=10$
$\therefore$ $a_1+a_2=\mathrm{10......}\left(2\right)$
Solving $\left(1\right)$ and $\left(2\right)$
$a_2=10$

$\therefore$ $a_2=10$

$a_n=a+(n-1)d$
$\therefore$ $a_1+d=10$ $\to$ $d=10$
$\therefore$ $a_{10}=a+9d$
$=0+9\left(10\right)=90$

$\therefore$ $a_{10}=90$.