Question

7: Find the formula for the geometric sequence 4, 20, 100, 500, ...

Answer 1

GIVEN:

We are given the following sequence of numbers;

`4,20,100,500,...`

Required;

To find the formula for the geometric series shown.

Step-by-step solution;

We first of all take note that the first term is 4, that is;

`a=4`

The common ratio can be derived by dividing each term by the previous one. That is,

`\begin{gathered} r=(20)/(4)=(100)/(20)=(500)/(100)=5 \\ \\ Therefore,\text{ }r=5 \end{gathered}`

To find the nth term of any geometric series, we shall use the formula which is given below;

`\begin{gathered} a_n=a\cdot r^(n-1) \\ \\ n=the\text{ }nth\text{ }term. \end{gathered}`

Where we now have the values of a and r, we can write up formula for the geometric series as follows;

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

Therefore,

ANSWER:

Option C is the correct answer