Question

Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -6 and 162, respectively.

Answer 1

nth term of a GS = a1r^(n-1)

where r = common ration

the r multiplies each term to get the next


so 6th term / 2nd term = r^4

Answer 2

sorry its 2nd and 5th

so we have 5th / 2nd = 162/ -6 = r^3

Answer 3

r^3 = -27

can you continue?

Answer 4

are we jus cubing the numbers?

Answer 5

yea

Answer 6

so r^3= 64

Answer 7

s r = cube root of -27

Answer 8

so r= 3

Answer 9

now - its -27

Answer 10

so -3

Answer 11

right
now you can find the first term and plug that and r into the formula

Answer 12

2 x (-3)^n-1

Answer 13

right

Answer 14

it might be better to leave the x out

nth term = 2(-3)^(n-1)