Use the recursively defined geometric sequence a1=56, an=4an−1 and find the common ratio.

Answer 1

To find the common ratio of a geometric sequence, we need to determine the ratio between any two consecutive terms.

Given that a₁ = 56 and aₙ = 4aₙ₋₁, we can find the second term, a₂, by plugging in n = 2:

a₂ = 4a₁
= 4 * 56
= 224

Now, we can find the common ratio by dividing a₂ by a₁:

common ratio = a₂ / a₁
= 224 / 56
= 4

Therefore, the common ratio of the geometric sequence is 4.