Writing and Using Explicit Rules for Geometric Sequences

We want to find the

8^{th}

term of the given geometric sequence. To do so, we will start by finding an explicit formula. Let's recall the general formula for a geometric sequence.

a_{n} = a_{1} \cdot r^{n - 1}

Now we will substitute the given values,

a_{1} = 1

and

r = 9,

into this formula.

a_{n} = 1 \cdot 9^{n - 1}

To find

a_{n}

when

n = 8,

we will substitute

8

for

n

in this formula.

a_{n} = 1 \cdot 9^{n - 1}

n = 8

a_{8} = 1 \cdot 9^{8 - 1}

Evaluate right-hand side

SubTermSubtract term

a_{8} = 1 \cdot 9^{7}

CalcPowCalculate power

a_{8} = 1 \cdot 4782969

IdPropMultIdentity Property of Multiplication

a_{8} = 4782969

Writing and Using Explicit Rules for Geometric Sequences 1.15 - Solution