Question

99th term of the series $2+7+14+23+34+..........$.is

• A. 9998
• B. 9999
• C. 10000
• D. none of these.

Answer 1

Answer: (A)

Let $S_n=2+7+14+23+34+.....+T_{n-1}+T_n$
Also $S_n=2+7+14+23+.....+T_{n-1}+T_n$
$\therefore 0=2+\left[5+7+9+11+......\left(n-1\right)terms\right]-T_n$
$\therefore T_n=2+\left[5+7+9+11+.....\left(n-1\right)terms\right]$
$=2+\frac{n-1}{2}\left[2\times 5+\left(n-2\right)2\right]$
$=2+\frac{n-1}{2}\left[10+2n-4\right]$
$2+\left(n-1\right)\left(n+3\right)$
$\therefore T_{99}=2+\left(98\right)\left(102\right)$
$=2+9996=9998$