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

  3.  an = 6n + 2

Step-by-step 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

___

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

  a2 = 6·2 +2 = 14

  a10 = 6·10 + 2 = 62

answer: howdy

step-by-step explanation: