Writing and Using Explicit Rules for Geometric Sequences

To determine

a_{6}

and

a_{1},

we'll substitute

n = 6

and

n = 11

in the formula and calculate. We start with

n = 6 .

a_{n} = 3 \cdot 2^{n - 1}

n = 6

a_{6} = 3 \cdot 2^{6 - 1}

SubTermSubtract term

a_{6} = 3 \cdot 2^{5}

CalcPowCalculate power

a_{6} = 3 \cdot 32

a_{6} = 96

Now calculate

a_{11} .

a_{n} = 3 \cdot 2^{n - 1}

n = 11

a_{11} = 3 \cdot 2^{11 - 1}

SubTermSubtract term

a_{11} = 3 \cdot 2^{10}

CalcPowCalculate power

a_{11} = 3 \cdot 1024

a_{11} = 3072

The elements are therefore

a_{6} = 96

and

a_{11} = 3072 .

Writing and Using Explicit Rules for Geometric Sequences 1.7 - Solution