Question

If the sum of the series 54, 51,48,45.......$T_n$ is 513, then the number of terms are

• A. 18
• B. 20
• C. 17
• D. None of these

Answer 1

The correct option is A 18

According to Conditions
$\Rightarrow 513=\frac{n}{2}\{2X54+(n-1\left)\right(-3\left)\right\}$
$\Rightarrow 1026=n(111-3_n)\Rightarrow 3n^2-{111}_n+1026=0$
$\Rightarrow (3_n-57)(n-18)=0$
Hence $n=18.$