Sum of the first n terms

## Sum of the first n terms

The sum of the first n terms is given by

S_n = frac(n(1_1 + a_n))(2)

which is the average of the first and last terms multiplied by the number of terms.

## Example 1

What is the sum of the first 50 terms of the sequence that begins 8, 11, 14, 17, 20, ...

8, 11, 14, 17, 20, …

The common difference is 3. The 0th term is 8 - 3 = 5

The nth term is 3n + 5

The 50th term is 3 x 50 + 5 = 155

 The sum of a sequence is S_n = frac(n(a_1 + a_n))(2) = frac(50(5 + 155))(2) = 4075

The nth term is given by 4n + 3.
 Sum of a sequence is S_n = frac(n(a_1 + a_n))(2) 2208 = frac(n(7 + a_n))(2) Substitute 4n+3 for a_n 2208 = frac(n(7 + (4n + 3)))(2) 4416 = 10n + 4n^2 0 = 4n^2 + 10n + 4416 Solve for n n = frac(-10 ± 266)(8) Only positive needed n = 32