Question

Identify the sequence graphed below and the average rate of change from n = 1 to n = 3.

coordinate plane showing the point 1, 8, point 2, 4, point 4, 1, and point 5, .5

Answer 1

\[a_1=8=2^3\]
\[a_2=4=2^2\]
\[a_4=1=2^0\]
\[a_5=0.5=2^{-1}\]
this one's not in there but you should see the pattern well enough to write the sequence
\[a_3=2=2^1\]

Answer 2

@peachpi those look like none of my question choices. im so confued

Answer 3

the pattern between points is multiplying by ½, so that's the common ratio, r.
The sequence is geometric. The formula for a geometric sequence is
\[a_n=a_1 r^{n-1}\]

Answer 4

r is ½.
a_1 is the first term of the sequence

Answer 5

Identify the sequence graphed below and the average rate of change from n = 1 to n = 3.

coordinate plane showing the point 1, 8, point 2, 4, point 4, 1, and point 5, .5

A) an = 8(one half)n − 1; average rate of change is −3
B) an = 10(one half)n − 1; average rate of change is 3
C)an = 8(one half)n − 1; average rate of change is 3
D) an = 10(one half)n − 1; average rate of change is −3

Those are my answer choices
@peachpi

Answer 6

ok. use the formula I just put up to get a formula for a_n