Question

Write the first five terms of the geometric sequence given that a₁ =2and a₂=12.

A. 2, 4, 8, 16, 32
B. 2, 6, 18, 54, 162
C. 2, 8, 32, 128, 512
D. 2, 10, 50, 250, 1250

Answer 1

The first five terms of the geometric sequence with a common ratio of 6, starting from a₁=2, are 2, 12, 72, 432, 2592.

Step-by-step explanation:

A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a constant factor called the common ratio. To find the common ratio, we can divide any term by the previous term. In this case, a₂/a₁ = 12/2 = 6. Therefore, the common ratio (r) is 6.

The first five terms of the geometric sequence can be found by multiplying each term by the common ratio:

1. a₁ = 2
2. a₂ = 2 * 6 = 12
3. a₃ = 12 * 6 = 72
4. a₄ = 72 * 6 = 432
5. a₅ = 432 * 6 = 2592

So, the first five terms of the geometric sequence are 2, 12, 72, 432, 2592.