Question

State whether the sequence is arithmetic or geometric, write a recursive and explicit formula and find the 10th term.
81, -27, 9, -3, 1...
Sequence Type: geometric
Recursive: _______
Explicit: ______
10th Term: -1/243

Answer 1

recursive: it just describes the pattern
"to get a new term, multiply the previous by -1/3

so term(n) = (-1/3)term(n-1)

explicit:
t(n) = a r^(n-1) <---- which is your formula for the general term
We have a = 81 and r = -1/3

t(n) = 81(-1/3)^(n-1) , but 81 = 3^4 or (-3)^4 AND (-1/3)^(n-1) = (-3)^(1-n)

t(n) = (-3)^4 * (-3)^(1-n)
= (-3)^(5-n)


check one of them:
t(3) = (-3)^2 = 9
Check some others if you wish

eg. term(10) = (-3)^-5
= 1/(-3)^5 = -1/243