Question

What is the formula for the sum of an arithmetic sequence?

Answer 1

To find the answer to this question, we should know about the arithmetic sequence. According to the definition, in the arithmetic sequence the difference between one term and the next is always constant. The general form of an arithmetic sequence is like this, \left\\{ a,a+d,a+2d,a+3d,... \right\\}, where $a$ is the first term and $d$ is the difference between the terms (called the ‘common difference’).

Complete step by step answer:
The sum of an arithmetic sequence is used to calculate the total of all the digits present in an arithmetic progression or series.
Formula for the sum of Arithmetic sequence:
Here are two formulas to calculate the sum of arithmetic sequence. Usually, the last term is given in the question, but in some questions, this is not given. So, for the calculation of the sum of arithmetic sequence, in which the last term is given, we can calculate the sum of arithmetic sequence using the below given formula:
$S=\dfrac{n}{2}\left( a+l \right)$
Where, ‘S’ is the sum of the arithmetic sequence,
‘a’ is the first term,
‘n’ is the total number of terms in the sequence, and
‘l’ is the last term of the sequence.
But if the last term of the sequence is not given, then we can calculate the sum of the arithmetic sequence by the given formula:
S=\dfrac{n}{2}\left\\{ 2a+\left( n-1 \right)d \right\\}
Where, ‘S’ is the sum of the arithmetic sequence,
‘a’ is the first term,
‘d’ is the common difference between the terms, and
‘n’ is the total number of terms in the sequence.

Note: Before solving the sum of the arithmetic sequence, we should find the last and first term in the question if they are provided. And then we should start the question. We have to be very careful while solving the question because sometimes we might end up making mistakes in considering a, d, n and l.