Question

Find the sum of the first six terms of the sequence. S6 = ⇒ 84

Answer 1

Answer:

Explained below.

Step-by-step explanation:

Consider the series is a set of first 6 natural numbers.

Sum of first n terms is:

$\text{Sum of n terms}=\frac{n(n+1)}{2}$

$\text{Sum of first 6 terms}=\frac{6(6+1)}{2}$

                               $=3\times7\\=21$

Consider the series is an arithmetic sequence.

Sum of first n terms is:

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

Here,

a = first term

d = common difference

Consider the series is an geometric sequence.

Sum of first n terms is:

$S_{n}=\frac{a_{1}\cdot(1-r^{n})}{(1-r)}$

Here,

a₁ = first term

r = common ratio