Question

Given the geometric sequence 3, 6, 12, 24, …, what is a1, the first term? What is r, the common ratio? Find the 8th term of this sequence. What formula did you use? Be sure to show your work.

Answer 1

\(\large a_1 = 3\) this is the first number in your sequence

r, hint* What number do you need to multiply to each previous number to get to the next?

Answer 2

can you explain more

Answer 3

Alright, so that a1 was pretty self explanatory so I'm assuming you have that! lol

So the 'r' the common ratio

We multiply each number by this 'r' to get to the following number

Here the sequence is 3,6,12,24 right?

To get from 3 to 6...what number do we multiply by?

Answer 4

2

Answer 5

Right, so our common ratio is 2

Just to check it is consistent

To get from 6 to 12 we also multiply by 2
and to get from 12 to 24 we again multiply by 2

Okay so good, we have our a1 and our 'r'

Now we need to find the 8th term right?

Answer 6

yep

Answer 7

Alright, so then to find any term of a geometric sequence, we use the formula

\[\large a_n = a_1 \times r^{n-1}\]

So here, since we want the 8th term...we simply plug in 8 for 'n'...still 2 for 'r' and still 3 for 'a1' so we have

\[\large a_8 = 3\times 2^{8-1}\]
\[\large a_8 = 3\times 2^{7} = ?\]

Answer 8

384

Answer 9

And that is correct!

Answer 10

thats it?

Answer 11

thanks

Answer 12

Yeah that is it! No problem!

Answer 13

can you help me with another problem?