Question

How do I find the partial sum of an arithmetic sequence?

Answer 1

Hint: The sum of an arithmetic sequence is denoted by $S_n$. It is the sum of all the “n” terms in an arithmetic progression. The partial sum of an arithmetic sequence is used when you have to add an “n” number of terms and it is very large and this partial sum of arithmetic sequence is used instead of placing all the values for “n”.

Complete step-by-step solution:
Arithmetic sequence is the sequence of the numbers in which each of the successive numbers is the sum of the previous number and the constant difference “d”. The arithmetic sequence is also known as the arithmetic progression and can be expressed as: $a_n=a_{n-1}+d$

First term in the arithmetic sequence can be expressed as: $a_1$
Nth term of the arithmetic sequence can be expressed as: $a_n=a_1+(n-1)d$
To find the partial sum of terms in the arithmetic sequence, follow below steps:
Find the first term of the arithmetic sequence - $a_1$
Find the nth term of the arithmetic sequence - $a_n$

To find sum of all the terms in the arithmetic progression, $S_n$
$S_n={\displaystyle \frac{n}{2}}(a_1+a_n)$
This is the required solution.

Note: Know the difference between the arithmetic and geometric progression and apply the concepts accordingly. In arithmetic progression, the difference between the numbers is constant in the series whereas, the geometric progression is the sequence in which the succeeding element is obtained by multiplying the preceding number by the constant and the same continues for the series. The ratio between the two remains the same.