Question

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

a)9999 b)9998 c)10000 d)9929

Answer 1

The Formula for the n th term of the sequence is

n^2 + 2n - 1

now the 99th ternm is 
99²+2(99) -1
9801+198-1
9998

the correct answer is option b)9998

Answer 2

Answer:

The 99th term of the given series is 9998.

Solution:

Given that

2 + 7 + 14 + 23 + 34 +...............

To find the nth term,

$\begin{array} { l } { 2 ^ { 2 } - 2 = 2 } \\\\ { 7 = 3 ^ { 2 } - 2 } \\\\ { 14 = 4 ^ { 2 } - 2 } \end{array}$

Therefore, nth term is

$=(n+1)^2-2$

By using $(a+b)^2$ formula,

$=n^2 +1+2n-2=n^2 +2n -1$

The 99th term is

$\begin{array} { l } { = \left( ( 99 ) ^ { 2 } + 2 \times 99 \right) - 1 } \\\\ { = 9801 + 198 - 1 } \\\\ { = 9801 + 197 } \\\\ { = 9998 } \end{array}$

Hence, the 99th term of the given series is 9998.