Question

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

Options

• \[S_n = n^2\]

• \[S_n = \frac{n}{2}(a + l)\]

• \[S_n = \frac{n}{2}[2a + (n-1)d]\]

• \[S_n = \frac{n(n+1)}{2}\]

Answer 1

If a, n, l are known, the sum is \[S_n = \frac{n}{2}(a + l).\] Here the first and last terms are averaged and multiplied by the number of terms n, so the common difference d is not needed.