# The sum of the first n terms of an arithmetic sequence is given by Sn=3n^2 - 2n. What is the common difference?

You need to remember that you may evaluate the common difference if you know any two consecutive terms of arithmetic progression.

Notice that the problem provides the sum of n terms, hence you may find the sum of n-1 terms such that:

`S_(n-1) = 3(n-1)^2 - 2(n-1)`

You need to...

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You need to remember that you may evaluate the common difference if you know any two consecutive terms of arithmetic progression.

Notice that the problem provides the sum of n terms, hence you may find the sum of n-1 terms such that:

`S_(n-1) = 3(n-1)^2 - 2(n-1)`

You need to expand binomial such that:

`S_(n-1) = 3n^2 - 6n + 3 - 2n + 2`

Collecting like terms yields:

`S_(n-1) = 3n^2 - 8n + 5`

You need to remember that you may find the n-th term `a_n ` such that:

`S_n - S_(n-1) = 3n^2 - 2n - 3n^2+ 8n- 5 = a_n`

Reducing like terms yields:

`S_n - S_(n-1) = 6n-5`

Hence, you may evaluate `a_(n-1) ` such that:

`a_(n-1) = 6(n-1) - 5`

`a_(n-1) = 6n - 6 - 5`

`a_(n-1) = 6n - 11`

You need to subtract `a_(n-1) ` from `a_n`  to find the common difference such that:

`a_n - a_(n-1) = 6n - 5 - 6n + 11`

Reducing like terms yields:

`a_n - a_(n-1) = 6`

Hence, evaluating the common difference yields d = 6.

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