Question

Consider the following sequence of numbers.

The common ratio of the sequence is =?
The sum of the first five terms of the sequence is=?

Blank 1 options: -1/3,-3,1/3,3
Blank 2 options: -303,183,-60,363

Answer 1

Blank 1 is -3

Blank 2 is 183

Explanation:

Let r be common ratio

`r = ( - 9)/(3) \\ r = - 3`

Sum of first 5 terms

`s = \frac{a( {r}^(n) - 1)}{r - 1} \\ s = \frac{ 3( {( - 3)}^(5) - 1) }{ - 3 - 1} \\ s = 183`

Answer 2

1) Second option: -3

2) Second option: 183

Explanation:

1) You can use any two consecutive terms to find the common ratio. This is given by:

`r=(a_n)/(a_(n-1))`

You can choose these consecutive terms:

`a_n=-9\\a_(n-1)=3`

Then the common ratio "r" is:

`r=(-9)/(3)=-3`

2) The sum of the first "n" terms can be found with this formula:

`S_n=(a_1(r^n-1))/(r-1)`

Since ther first term is 3 and you need to find the sum of the first 5 terms, then:

`a_1=3\\n=5`

Substituting into
`Sn=(a_1(r^n-1))/(r-1)`, you get:

`S_((5))=(3((-3)^5-1))/(-3-1)=183`