Answer to Sequence Problem: Eighth Term

[2015HuntMJ]

Homework Statement

36, 4, 20, ...

The first term of the sequence above is 36, and the second term is 4. Each term after the second is the average (arithmetic mean) of the two preceding terms. Which term of the sequence is the first that is not an integer?

a. the fourth term
b. the fifth term
c. the sixth term
d. the seventh term
e. the eighth term

Homework Equations

The Attempt at a Solution

(36 + 4) / 2 = 20
(20 +4) / 2 = 12
(12+20) / 2 = 11
(11+12) / 2 = 7.5

So...
36, 4, 20, 12, 11, 7.5

The answer should be the sixth term? But the answer sheet says it should be e. the eighth term.

 

[Fredrik]

Homework Statement

36, 4, 20, ...

The first term of the sequence above is 36, and the second term is 4. Each term after the second is the average (arithmetic mean) of the two preceding terms. Which term of the sequence is the first that is not an integer?

a. the fourth term
b. the fifth term
c. the sixth term
d. the seventh term
e. the eighth term

Homework Equations

The Attempt at a Solution

(36 + 4) / 2 = 20
(20 +4) / 2 = 12
(12+20) / 2 = 11
(11+12) / 2 = 7.5

So...
36, 4, 20, 12, 11, 7.5

The answer should be the sixth term? But the answer sheet says it should be e. the eighth term.

(12+20)/2 is not 11, and (11+12)/2 is not 7.5.