The first term of a geometric sequence is 3, and the second term is 6. What is the 5th ter… — ACT

The first term of a geometric sequence is $3$ , and the second term is $6$ . What is the $5$ th term of this sequence?

The fifth term of the sequence is

48

The first term of the geometric sequence is

a_1 = 3

, and the second term is

a_2 = 6

. The common ratio

r

6 \div 3 = 2

. The

n

th term of a geometric sequence is given by

a_n = a_1 \cdot r^{n-1}

. For the fifth term (

n=5

), the calculation is

3 \cdot 2^{5-1} = 3 \cdot 2^4 = 3 \cdot 16 = 48

. This matches the correct value.

Find the common ratio (

r

) of the geometric sequence.

r = \frac{6}{3} = 2

The common ratio of a geometric sequence is found by dividing any term by the preceding term.

Apply the formula for the

n

th term of a geometric sequence,

a_n = a_1 \cdot r^{n-1}

, to find the fifth term.

a_5 = 3 \cdot 2^{5-1} = 3 \cdot 2^4

We substitute

a_1 = 3

r = 2

, and

n = 5

into the standard formula.

Evaluate the expression.

a_5 = 3 \cdot 16 = 48

Calculate

2^4 = 16

first, then multiply by

3

according to the order of operations.

Finding a specific term in a geometric sequence using the general formula

Question