Question

an={3ⁿ}{2^ⁿ⁺¹} The nth term of a sequence is given. Determine if the series is arithmetic or geometric. Find the common difference or the common ratio.

Answer 1

The given sequence is geometric and the common ratio is 6.

Step-by-step explanation:

The given sequence is an={3ⁿ}{2^ⁿ⁺¹}. To determine if it is arithmetic or geometric, we need to check if the ratio of consecutive terms is constant. Let's find the ratio of the second term to the first term:

r = a₂/a₁ = (3²)(2³)/(3¹)(2²) = 9(8)/3(4) = 6.

Since the ratio is constant (6), the sequence is geometric. The common ratio is 6.