Question

For the geometric sequence, the common ratio is 2 and the 12th term is a12 =6144. What is the first term?

A. a1=2

B.a1=3

C.a1=4

D.a1=5

Answer 1

B. a1 = 3

Explanation:

Since we have the comon ratio and 12th term, we could just divide the 12th term (6144) by 2 11 times until we get to the 1st term:

`6144 /2/2/2/2/2/2/2/2/2/2/2 = 3`

For a better understanding of the question, let's use the formula for geometric equations:

a(r)^(n-1)

1. Let's plug in the values we know

• r = common ratio = 2

• n = 12

a(2)^(12-1)

2. Set equation equal to 6144 (Since we use n = 12) and solve for a

• a = 6144/ (2^11)
• a = 3

To confirm this, let's use the formula for geometric equations again:

a(r)^(n-1)

a = first term = 3

r = common ratio = 2

3(2)^(12-1) = 6144

Therefore, a1 = 3