Question

If the $10$th term of an A.P is $21$ and the sum of its first ten terms is $120$, find its $n$th term.

• A. $7n+1$
• B. $5n+1$
• C. $2n+1$
• D. None of these

Answer 1

Answer: (C)

$2n+1$

Given,

$a_{10}=21$

$a+(10-1)d=21$

$a+9d=21$....(1)

$S_{10}=120$

$\frac{10}{2}[2a+(10-1\left)\right]d=120$

$2a+9d=24$......(2)

solving (1) and (2), we get,

$a=3$

from (2), we have,

$d=2$

$a_n=a+(n-1)d$

$a_n=3+(n-1)2$

$\therefore a_n=2n+1$