Question

What is the sum of the first 80 terms of the sequence 53, 54, 55, 56, ...?

Answer 1

7,400

Explanation:

First, we have to see that this is an arithmetic sequence... since to get the next element we add 1 to it. (a geometric sequence would be a multiplication, not an addition)

So, we have a, the first term (a = 53), and we have the difference between each term (d = 1), and we want to find the SUM of the first 80 terms.

To do this without spending hours writing them down, we can use this formula:

`S = (n)/(2) * (2a + (n - 1) * d)`

If we plug in our values, we have:

`S = (80)/(2) * (2 * 53 + (80 - 1) * 1) = 40 * (106 + 79 * 1)`

S = 40 * (106 + 79) = 40 * 185= 7,400