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)

9998

Answer 2

Let $S_{n} = 2+7+14+23+34+..... +T_{n-1} +T_{n}$ Also $S_{n} = 2+7+14+23+.....+T_{n-1} +T_{n}$ $\therefore 0 = 2+ \left[5+7+9+11+......\left(n-1\right) terms\right] - T_{n}$ $\therefore T_{n} = 2+\left[5+7+9+11+.....\left(n-1\right) terms\right]$ $= 2+\frac{n-1}{2} \left[ 2\times5+\left(n-2\right)2\right]$ $= 2+\frac{n-1}{2} \left[10+2n-4\right]$ $2+\left(n-1\right)\left(n+3\right)$ $\therefore T_{99} = 2+\left(98\right)\left(102\right)$ $= 2+9996 = 9998$