# The sum of the first 10 terms of an arithmetic sequence is 530. What is the first term if the last term is 80? What is the common difference?

by Rasulowang

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by Rasulowang

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Common difference is 6.

Solution below. (sorry for the handwriting)

Solution below. (sorry for the handwriting)

Note that you are given the following data:

You are asked of the 1st term(A1) and the common difference(d).

In finding the nth term of an arithmetic progression, we use the formula:

Using the given data we'll have:

In finding the Sum of all the terms, we use the formula:

Substituting the given values we'll have:

Substitute equation 1 to equation 2