Question

In an arithmetic sequence, the seventh term is −9 and the nineteenth term is 39.

Find the common difference. Give only the exact value as your answer.

Answer 1

d = 4

Explanation:

a7 = -9

a19 = 39

We know the formula for an arithmetic sequence is

an = a1+d(n-1)

Using the givens:

a7 = -9 = a1 +d(7-1)

a19 = 39 =a1 +d(19-1)

Subtracting these equations

-9 = a1 +d(6)

39 =a1 +d(18)

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-48 = 0 -12 d

Divide by -12

4 =d