Question

What is the 15th term in the sequence?

3, 12, 48, 192, 768, . . .

Answer 1

iknow the answer i just need to know if its right

Answer 2

i know the ratio to 3 and 12 is 9 but now i see theirs 48 and 192 so i dont understand it now

Answer 3

Two types of sequences are arithmetic and geometric.
In an arithmetic sequence, the same number is added to each term to get the following term.
In a geometric sequence, the same number is multiplied by each term to get the following term.

Answer 4

oooh so 9 is being multiplied

Answer 5

First, we need to find out if this is an arithmetic sequence or a geometric sequence.
If this is an arithmetic sequence, then you are ***adding*** the same number to each term to get the next term.
What do you add to 3 to get 12?
What do you add to 12 to get 48?
Are they the same number in each case?

Answer 6

no

Answer 7

9 is not being multiplied. 9 * 3 is not equal to 12

Answer 8

this is a geometric progression
to get from one number to the next in the sequence you multiply by the same factor
this factor is called the common ratio

Answer 9

Correct. 3 + 9 = 12
12 + 36 = 48
Since 9 and 36 are definitely not the same number, this is not an arithmetic sequence.

Answer 10

Now let's determine if this is a geometric sequence.
In a geometric sequence, we multiply each term by the same number to get the next term.
What do you multiply 3 by to get 12?

Answer 11

4

Answer 12

Great.
What do you multiply 12 by to get 48?

Answer 13

just like the other problem
when you divide you will find r
the first term is a is given =3

Answer 14

4

Answer 15

Great.
If you continue to multiply by 4, you will get 192, 768, 3072, etc.

Answer 16

what would i be dividing @triciaal

Answer 17

Now we know this is a geometric sequence.
One way of finding the 15th term is to just keep multiplying each term you get by 4 and counting the terms until you get to the 15th term.

Answer 18

thank you im writing this stuff down so give me one second

Answer 19

Another way of doing it is to use a formula.
Here is the formula to find the nth term:
\(a_n = a_0r^{n - 1}\)
where \(a_0\) is the first term; \(r\) is the common ratio; \(a_n\) is the desired \(n^{th} \) term.

Answer 20

and what is the common ration in this case?

Answer 21

4

Answer 22

@mathstudent55 i solved the equation and i got 201326592 is this correct?

Answer 23

@Nnesha

Answer 24

I get 805,306,368
I multiplied by 4 one more time than you did.

Answer 25

@MiggityMiggityMac yes^^^^that's what i'm telling u