Question

If the sum of the series is 60100, then the number of terms are.

• A. 100
• B. 200
• C. 150
• D. 250

Answer 1

Answer: (B)

200

Answer 2

Series, $2 + 5 + 8 + 11 + \ldots \ldots$

$a = 2 , d = 3$ and let number of terms is $n$ then sum of

A.P. $= \frac { n } { 2 } \{ 2 a + ( n - 1 ) d \}$

$\Rightarrow$ $60100 = \frac { n } { 2 } \{ 2 \times 2 + ( n - 1 ) 3 \}$ $\Rightarrow$ $120200 = n ( 3 n + 1 )$

$\Rightarrow$ $3 n ^ { 2 } + n - 120200 = 0$ $\Rightarrow$ $( n - 200 ) ( 3 n + 601 ) = 0$

Hence $n = 200$ .