Question

Find the sum of first 20 terms of the sequence whose nth term is $2n+3n$

• A. 1050
• B. 645
• C. 1100
• D. 1000

Answer 1

The correct option is A 1050

Given:$a_n=2n+3n$

Put $n=1$ in $a_n$, we get

$a_1=2\left(1\right)+3\left(1\right)=2+3=5$

Put $n=2$ in $a_n$, we get

$a_2=2\left(2\right)+3\left(2\right)=4+6=10$

Put $n=3$ in $a_n$, we get

$a_3=2\left(3\right)+3\left(3\right)=6+9=15$

So, Given A.P is $5,10,15,....$

Hence, $a=5$ and $d=a_2-a_1=10-5=5$

Now, Sum of first $20$ terms is given by

$S_{20}=\frac{n}{2}[2a+(n-1\left)d\right]$

$\Rightarrow S_{20}=\frac{20}{2}\left[2\right(5)+(20-1\left)\right(5\left)\right]$

$\Rightarrow S_{20}=10[10+19(5\left)\right]$

$\Rightarrow S_{20}=1050$

So, $\text{A}$ is the correct option.