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