Question

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

Answer 1

Answer:

Common difference(d) is:

$a2-a1=a3-a2=a4-a3= d$

d is constant till  

$a_n-a_n_-_1 =d$

Step-by-step 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:

              $S_n=\frac{n}{2} [2a+(n-1)d]$