Equation of Geometric Sequence

In this article, we will discuss the equation of geometric sequence. Geometric sequence is defined as, the sequence of a numbers such that the ratio between two consecutive members of the sequence is a constant.

Formulas for geometric sequence:

nth term of the sequence: a_n = a_1 * r^(n-1)

Series of the sequence: S_n = (a_1(1-r^n))/(1 - r)

The equation of geometric sequence example problems are given below.


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Example Problems for Equation of Geometric Sequence:

Example problem 1:

Find out the 6th term of a geometric sequence if a1 = 72 and the common ratio (C.R) r = 2

Solution:

Use the formula a_n = a_1 * r^(n-1) that gives the nth term to find a_6 as follows

"a_6 = 72 * (2)^(6 - 1)

= 72 * (2)5

= 72 * 32

After simplify this, we get

= 2304

The 6th term of a geometric sequence is 2304

Example problem 2:

Find out the 7th term of a geometric sequence if a1 = 31 and the common ratio (C.R) r = 2

Solution:

Use the formula a_n = a_1 * r^(n-1) that gives the nth term to find a_7 as follows

"a_7 = 31 * (2)^(7 - 1)

= 31 * (2)6

= 31 * 64

After simplify this, we get

= 1984

The 7th term of a geometric sequence is 1984.
More Example Problems for Equation of Geometric Sequence:

Example problem 3:

Find out the 11th term of a geometric sequence if a1 = 42 and the common ratio (C.R) r = 2

Solution:

Use the formula a_n = a_1 * r^(n-1) that gives the nth term to find a_11 as follows

"a_11 = 42 * (2)^(11 - 1)

= 42 * (2)10

= 42 * 1024

After simplify this, we get

= 43008

The 11th term of a geometric sequence is 43008.


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Example problem 4:

Find out the 18th term of a geometric sequence if a1 = 58 and the common ratio (C.R) r = 2

Solution:

Use the formula a_n = a_1 * r^(n-1) that gives the nth term to find a_18 as follows

"a_18 = 58 * (2)^(18 - 1)

= 58 * (2)17

= 58 * 131072

After simplify this, we get

= 7602176

The 18th term of a geometric sequence is 7602176

The above example problems are helpful to study of geometric sequence equation.