Question

How do you determine the common difference for an arithmetic sequence?

Answer 1

Common difference(d) is:

`a2-a1=a3-a2=a4-a3= d`

d is constant till

`a_n-a_n_-_1 =d`

Explanation:

An arithmetic sequence or arithmetic progression is the sequence, whose difference of consecutive terms called common difference is constant throughout the sequence.

Considering, the sequence
`a_1,a_2,a_3,a_4,.......a_n`

`a2-a1=a3-a2=a4-a3= d`

d= common difference.

we can find any
`n^t^h` term in the sequence by using the formula

`a_n=a_1+(n-1)d`

where
`a_n`= any
`n^t^h` term

`n\\`=Number of terms

`d`=common difference

`a_1`= first term

Also sum of n terms of A.P can be find by the formula:

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