Determine if the sequence is geometric Do you multiply or di

Determine if the sequence is geometric (Do you multiply or divide the same amount from one term to the next?) Find the common ratio (The number you multiply or divide) Create an explicit formula using: a_n = a_1 (r)^n - 1 Ex: Sequence: {3, 6, 12, 24, 48, 96, ...}. Find an explicit formula. Makers of Japanese swords in the 1400s repeatedly folded and hammered the metal to form layers. The folding process increased the strength of the sword. The table shows how the number of layers depends on the number of folds. Write a recursive rule and an explicit rule for the geometric sequence by the table. A. Find the common ratio by calculating the ratios of consecutive terms. 4/2 = 8/4 = 16/8 = 32/16 = The common ratio, r, is _____.

Solution

A. The common ratio is calculated here:

4/2 = 2
8/4 = 2
16/8 = 2
32/16 = 2

The common ratio,r =2