Question

Suppose that in a sequence a2 = 14, a4 = 26, a6 = 38, a8 = 50, and a10 = 62. Which of the following is the explicit formula for the sequence?

1. an = 2n + 6
2. an = 2n + 12
3. an = 6n + 2
4. an = 12n + 2

Answer 1

3. an = 6n + 2

Explanation:

The differences between given terms are 12:

26 -14 = 12

38 -26 = 12

...

Since these terms are two terms apart in the sequence, the common difference in the arithmetic sequence must be 12/2 = 6.

The only answer choice that has 6 as a common difference is ...

an = 6n +2

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Checking a couple of terms, we find this expression matches:

a2 = 6·2 +2 = 14

a10 = 6·10 + 2 = 62