Question

Find $T_{50}if{T}_n$ denotes $n^{th}$ term of the series $2+3+6+11+.....$

Answer 1

Now, the difference of the terms of this series is in AP

$3-2=1$

$6-3=3$

$11-6=5$

$18-11=7$

So the series of the difference $=1,3,5,7$

$2+1=3$

$2+1+3=6$

$2+!+3+5=11$

$2+1+3+5+7=18$ and so on....

So we can say, $n$th term of given series is =sum of (n-1) terms of $(1,3,5,7)+2$

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

$a=1,n=49,d=2$

$S_{49}=\frac{49}{2}[2+(49-1\left)2\right]$

$=49\left(49\right)$

$={49}^2$

$T_{50}$ of series $2+3+6+11+.....=2+{49}^2$

$=2+2401=2403$