Question

When the first term a, the number of terms n and the common difference d are known, which formula gives the sum of the first n terms of an Arithmetic Progression?

Options

• \[S_n = n(n+1)\]

• \[S_n = \frac{n}{2}[2a + (n-1)d]\]

• \[S_n = \frac{n(n+1)}{2}\]

• \[S_n = \frac{n}{2}(a + l)\]

Answer 1

If a, n, d are known, the sum is \[S_n = \frac{n}{2}[2a + (n-1)d].\] This form uses the common difference d in place of the last term l.