Find the specified term of the geometric sequence.

Question

a) Find the specified term of the geometric sequence.

7th term: 2, 12, 72, . . .

Answer 1

The nth term of a geometric sequence is a_n = a_1 * r^n-1.

Here your a_1, or first term, is 2, and the r, or common ratio, is 6 (since each term gets multiplied by 6 to get the next one). Plugging into the formula:

a_7 = 2 * 6^7-1 = 2 * 6⁶ = 2 * 46656 = 93312.