Question

What is an arithmetic sequence?

Answer 1

Hint: An arithmetic sequence is a sequence ( a sequence can simply be said to as the list of numbers when talking in mathematical sense) that has same common difference between its two successive terms (The common difference can be positive or negative it just has to be same in every successive term).

Complete step by step solution:
An arithmetic sequence is a sequence ( a sequence can simply be said to as the list of numbers when talking in mathematical sense) that has some common difference between its two successive terms
We will now see a few examples of arithmetic sequences so that the concept can be internalized.
 $ 4,8,12,16,20 $ can be said to be as an arithmetic sequence the main reason is that the consecutive terms in the sequence are all $ 4 $ apart from each other . That means that the common difference of this arithmetic sequence is $ 4 $
We will now see another example of an arithmetic sequence,
  $ 13,26,39,52,65 $ is another arithmetic sequence because every consecutive term is $ 13 $ apart from each other . so the common difference is $ 13 $ .
For a sequence to be an arithmetic sequence the common difference has to be the same across all the successive terms .

Note: Arithmetic sequences are also called as arithmetic progression,
The sum for $ n $ terms of a arithmetic sequence is stated here,
\[{S_n} = \dfrac{{n(a + l)}}{2}\]
Where $ a $ is the first term of the arithmetic sequence and $ l $ is the last term of the arithmetic sequence , the term $ n $ is the number of terms whose sum has to be found out.