## anonymous one year ago 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.

1. johnweldon1993

$$\large a_1 = 3$$ 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?

2. anonymous

can you explain more

3. johnweldon1993

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?

4. anonymous

2

5. johnweldon1993

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?

6. anonymous

yep

7. johnweldon1993

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

8. anonymous

384

9. johnweldon1993

And that is correct!

10. anonymous

thats it?

11. anonymous

thanks

12. johnweldon1993

Yeah that is it! No problem!

13. anonymous

can you help me with another problem?