Expert: Sherman D. - 1/17/2009

Question
I need to tell whether the following sequence is arithmetic, geometric, or neither. Then find the next two terms in the sequence and show how I arrived at my answer.
The sequence is: 12,16,25,34,43...

Answer
12, 16, 25, 34, 43

a(n) = a1 + d(n - 1)

a(2) = 12 + d(2 - 1)
16 = 12 + d

d = 4

a(3) = 12 + d(3 - 1)
25 = 12 + 2d
2d = 13
d = 13/2

so its not arithmetic

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a(n) = a1 * r^(n - 1)

a(2) = 12 * r^(2 - 1)
16 = 12 * r
r = 4/3

a(3) = 12 * r^(3 - 2)
25 = 12 * r^2
r^2 = 25/12
r = (5sqrt(3))/6

so its not geometric

there probably is a pattern. i recommend going to answers.yahoo.com to see if they come up with one.