# Write the 50th term of the series 2 + 3 + 6 + 11 + 18 + ...

Question:

Write the 50th term of the series 2 + 3 + 6 + 11 + 18 + ...

Solution:

We have,

$a_{1}=2$

$a_{2}=3=2+1$

$a_{3}=6=2+1+3$

$a_{4}=11=2+1+3+5$

.

.

$a_{50}=2+1+3+5+\ldots(50$ terms $)$

$=2+\frac{49}{2}[2 \times 1+(49-1) \times 2]$       (As, the terms apart 2 are in A.P. with $a=1$ and $d=2$ )

$=2+\frac{49}{2}(2+48 \times 2)$

$=2+\frac{49}{2} \times 98$

$=2+49^{2}$

$=2+2401$

$=2403$

So, the 50th term of the given series is 2403.