Question

How do you find the sum of n terms in an arithmetic sequence?

Answer 1

with the help of formula

Sn=n/2[2a+(n-1)d]

Sn=n/2(d+l)

Sn=n/2(t1-tn)

Answer 2

An arithmetic sequence (AP) is a series of values that differs with a constant values.

Generally, the position of an unknown term is considered as an nth term. Now, adding the sequence up to to the nth term can be genrallised as $S_n$,

$S_n=n(\frac{a_1+a_n}{2})$ ,  

Here, the initial terms is denoted by $a_1$ and further terms are denoted as $a_I$ and i is their positions. So $a_n$ is the nth terms representation.

E.g.: Find the sum of first 20 terms if $a_1=5$ and $a_20=62$  

$S_20=\frac{20(5+62)}{2}$  

$S_20=670$