Activity › Discussion › Math › Sequence › Reply To: Sequence

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To find the common difference (d) in an arithmetic progression (A.P.) when the sum of the first ‘n’ terms (Sn) is given, we can use the following formula:
Sn = (n/2) * [2a + (n1)d]
where ‘a’ is the first term and ‘d’ is the common difference.
In the given problem, Sn = 3n^2 + 2n.
Substituting this into the formula, we have:
3n^2 + 2n = (n/2) * [2a + (n1)d]
Simplifying further:
3n^2 + 2n = (n/2) * [2a + nd – d]
Now, let’s equate the coefficients of n^2 and n on both sides:
3 = d/2
Multiplying both sides by 2, we get:
6 = d
Therefore, the value of ‘d’ in the arithmetic progression is 6.