the first term of an arithmetic sequence is 2 and the sum of the first 15 terms is 292.5. Find the common difference

Given:

First term of an arithmetic sequence is 2.

Sum of first 15 terms = 292.5

To find:

The common difference.

Solution:

We have,

First term:

Sum of first 15 terms:

The formula of sum of first n terms of an AP is

Where, a is first term and d is common difference.

Putting , n=15 and a=2 in the above formula, we get

Divide both sides by 15.

Dividing both sides by 7, we get

Therefore, the common difference is 2.5.

answer: .64

step-by-step explanation

set up the formula for standard deviation for this set of numbers, then simplify