Question

Find an explicit formula for a sequence of the form a1, a2, a3, with the initial terms given below: 5, 10, 20, 40, 80, 160, 320

Answer 1

The explicit formula for the geometric sequence with the given terms is an = 5 * 2n-1.

Step-by-step explanation:

The sequence given is a geometric sequence where each term is twice the previous term. To find an explicit formula for the geometric sequence, we recognize that the ratio between consecutive terms is constant. The sequence is 5, 10, 20, 40, 80, 160, 320. The common ratio (r) is 2, and the first term (a1) is 5.

We can use the formula for the nth term of a geometric sequence, which is given by an = a1rn-1. Therefore, the explicit formula for this sequence is an = 5 * 2n-1.