What is the 32nd term of the arithmetic sequence -12 -7?

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1

this is a geometric sequence with common ratio r

r = = = = 3

(a)

to obtain a term in the sequence multiply the previous term by 3

= 3 ← recursive rule

(b)

the n th term of a geometric sequence is

=

where is the first term and r the common ratio

= 6 × ← explicit rule