Question

Find the formula for the geometric sequence 4, 20, 100, 500,...OA. = 4()-1OB.a, 4.5-1Oc.a,20()"-1OD. a, 20(-)"=Reset Selection

Answer 1

The general formula of a geometric sequence is expressed as

`\begin{gathered} a_n=a_1* r^(n-1) \\ where \\ a_1\Rightarrow first\text{ term of the sequence} \\ r\Rightarrow common\text{ ratio} \end{gathered}`

Given the geometric sequence:

`4,\text{ 20, 100, 500, . . .}`

where

`\begin{gathered} a_1=4 \\ r=(a_2)/(a_1)=(20)/(4)=5 \end{gathered}`

By substitution, we have

`a_n=4*5^((n-1))`

Hence, the formula of the geometric sequence is

`a_n=4\cdot5^(n-1)`

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