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

Answer:

Blank 1 is -3

Blank 2 is 183

Step-by-step explanation:

Let r be common ratio

$r = \frac{ - 9}{3} \\ r = - 3$

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

Answer:

1) Second option: -3

2) Second option: 183

Step-by-step explanation:

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

$r=\frac{a_n}{a_{n-1}}$

You can choose these consecutive terms:

$a_n=-9\\a_{n-1}=3$

Then the common ratio "r" is:

$r=\frac{-9}{3}=-3$

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

$S_n=\frac{a_1(r^n-1)}{r-1}$

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  $Sn=\frac{a_1(r^n-1)}{r-1}$, you get:

 $S_{(5)}=\frac{3((-3)^5-1)}{-3-1}=183$