In a geometric sequence of positive numbers, the first term is 3 and the common ratio is 2… — GMAT

In a geometric sequence of positive numbers, the first term is $3$ and the common ratio is $2$ . What is the value of the 5th term of this sequence?

The 5th term of the sequence is

48

The

n

-th term of a geometric sequence is given by

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

. Substituting

a_1 = 3

r = 2

, and

n = 5

gives

a_5 = 3 \cdot 2^4 = 3 \cdot 16 = 48

Identify the formula for the

n

-th term of a geometric sequence.

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

In any geometric sequence, each term is obtained by multiplying the previous term by the common ratio

r

Substitute the given values into the formula.

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

The first term

a_1 = 3

, common ratio

r = 2

, and term number

n = 5

Calculate the exponent and final value.

a_5 = 3 \cdot 16 = 48

Evaluate

2^4 = 16

first according to order of operations, then multiply by 3.

Geometric Sequence

n

-th Term Formula

Question