Question

find the sum to n terms of the series 3+5+9+15+23+...

Answer 1

the sum to n terms is 55

Answer 2

The sum of n terms of the sequence 3+5+9+15+23+... is 2n + n².

• The given terms are 3+5+9+15+23+.....

• As we can see that the difference between consecutive terms of the series is increasing in multiples of 2.

• Therefore,

We write the sum of the series using general term is as :

Sum to n terms = $\sum_{n=1}^n$ (1 + 2n)

• Now,

$\sum_{n=1}^n$ (1 + 2n)

= $\sum_{n=1}^n 1 + 2 \sum_{n=1}^n n$

= n + 2 $\frac{n(n+1)}{2}$

= n + n(n+1)

= n + n² + n = 2n + n²

• Sum of n terms of the series is 2n + n².