What is the 14th term of the geometric sequence.

Question

3, 6, 12, 24, ...

a₁₄ = ________

Answer 1

A Geometric Sequence has a Common Ratio (r) between adjacent terms. That means, for example:

, a₂ / a₁ = 2

So, a₂ = 2a₁ and

a₁₄ = 2(2(2(2(2(2(2(2(2(2(2(2(2a₁) ... [fill in intermediate values]

a₁₄ = 3*2¹³ ... [put a₁ at beginning]

a_n = a₁r^n-1

a₁₄ = 24,576

Answer 2

6/2 = 2

12/6 = 2

The common ratio, r, is 2.

The first term, a₁=3

Using the formula for geometric series

an=a₁(r)^n-1

Plugging in values:

a₁₄=3(2)^14-1

a₁₄=3(2)¹³ = 24576