The defining characteristic of all geometric sequences is a common ratio which is a constant when dividing any term by the term preceding it.

In this case the common ratio is: -6/9=4/-6=r=-2/3

An infinite series will have a sum when r^2<1, so in this case the sum will converge to an actual value because (-2/3)^(+oo) approaches zero.

The sum of any geometric sequence is:

s(n)=a(1-r^n)/(1-r), since we have a common ratio of -2/3 and we want to calculate an infinite series, ie, n approaches infinity, the sum becomes simply:

s(n)=a/(1-r) (because (1-r^+oo) approaches 1 as n approaches +oo)

So our infinite sum is:

s(+oo)=9/(1--2/3)

s(+oo)=9/(1+2/3)

s(+oo)=9/(5/3)

s(+oo)=27/5

s(+oo)=54/10

s(+oo)=5.4

7 0

4 years ago

What is 2 over 3 x 18

zimovet [89]

Answer:

1 over 32

Step-by-step explanation:

you multiply 3 by 18 to get 64 then simplify by dividing by 2

6 0

3 years ago

Round 7,298,341 to the nearest 10,000

WITCHER [35]

8,300,000 is your answer because 8 is higher then five so you add one to 9 which make it ten so u have to add one more to 200,000

5 0

3 years ago

Read 2 more answers

A store sells gift cards in preset amounts.You can purchase gift cards for $10 or $25. You have spent $285 on gift cards. Erie a

pav-90 [236]

Answer:

10x + 25y = 285

One $25 gift cards with 26, $10 gift cards.

Three $25 gift cards with 21, $10 gift cards and

Five $25 gift cards with 16, $10 gift cards.

Step-by-step explanation:

I can purchase gift cards for $10 or $25. I have spent $285 on gift cards.

If I have purchased x number of $10 gift cards and y number of $25 gift cards then the equation that models the situation in standard form will be given by

10x + 25y = 285 .......... (1)

Now, for y = 1, x = 26

For, y = 3, x = 21

For, y = 5, x = 16

So, here are the three combinations of gift cards that I could have purchased.

One $25 gift card with 26, $10 gift cards.

Three $25 gift cards with 21, $10 gift cards and

Five $25 gift cards with 16, $10 gift cards. (Answer)

8 0

3 years ago