## sydneygill14 3 years ago Identify the 12th term of a geometric sequence where a1 = 8 and a6 = –8,192.

1. tmauldin

do you have a2

2. sydneygill14

no i dont

3. amistre64

since youve gone thru this with alot of people already ... what is the general equation for an arith. progression ?

4. tmauldin

a2=-32

5. tmauldin

an= ar1 * r^(n-1) this is the geometric equation

6. amistre64

lol ... its just too easy to read over that word :) yes, this is a geo ... good eye

7. tmauldin

lol, i see it now

8. tmauldin

a12=-33554432

9. tmauldin

this is how i found it, give me a moment i will explain

10. tmauldin

since the formula for any term is given by an= a1 *r^(n-1) in order to find any term you must know a1 and r you have a1 but we need to find r, in order to find r we need an and a1 we only have a1 and a6 so substitute a6 for an in the above formula a6=8*r ^(6-1) -8192=8 * r ^(5) -1024=r^5 -4=r now using above formula again we have a12=8 * (-4)^(12-1) a12=8 * (-4)^11 a12=8 * (-4194304) a12=-33554432 hint* any time a term is negative, the ratio will be negative

11. tmauldin

formula for finding any term in ageometric sequence an=a1*r^(n-1) i have never worked a related problem, so that is why it took so long, but now we both know amistre64 helped me realize you needed a12 good day

12. tmauldin

geometric equation a.k.a arithmetic transformation