In a geometric sequence with a first term of 4 and a third term of 16, what is the second term?

• A. 6
• B. 10
• C. 8
• D. 12

Answer: (C)

In a geometric sequence, each term is derived by multiplying the previous term by a constant known as the common ratio. Given that the first term is 4 and the third term is 16, we can define the terms of the sequence as follows:

• The first term (a1) is 4.

• The second term (a2) can be expressed as ( a1 \times r ), where r is the common ratio.

• The third term (a3) can be expressed as ( a2 \times r ) or ( a1 \times r^2 ).

From the information given, we have:

1. The first term: ( a1 = 4 )

2. The third term = ( a1 \times r^2 = 16 )

Substituting the value of the first term into the equation for the third term, we have:

[ 4 \times r^2 = 16 ]

To isolate ( r^2 ), divide both sides by 4:

[ r^2 = \frac{16}{4} = 4 ]

Now, taking the square root of both sides yields:

[ r = 2 ] (the positive square root is