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The first term of an arithmetic sequence is -4. The 8th term is 10. What is the common difference?

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4 votes

Answer:

2

Explanation:

The general term of an arithmetic sequence is given by the explicit formula ...

an = a1 +d(n -1)

The first term is a1 = -4, and the 8th term is a8 = 10. Using these numbers in the formula, we find ...

a8 = a1 +d(8 -1) . . . . put n=8 into the formula

10 = -4 + 7d . . . . . . . fill in the other known values

14 = 7d . . . . . . . . . . . add 4

2 = d . . . . . . . . . . . . . divide by 7

The common difference is 2.

_____

You may have noticed that the difference between the first and eighth terms is 8-1 = 7 times the common difference. And, our solution is ...

d = (10 -(-4))/7 = 2

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