Problem 1
Answer: 12288
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Explanation:
The first term is a = 3 and the common ratio or multiplier is r = 4. We start with 3 and multiply each term by 4 to get the next one. The nth term of this geometric sequence is
a(n) = a*(r)^(n-1)
a(n) = 3*(4)^(n-1)
Plug in n = 7 to get the seventh term
a(7) = 3*(4)^(7-1)
a(7) = 3*(4)^6
a(7) = 3*4096
a(7) = 12288
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Problem 2
Answer: 1/2 or 0.5
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Explanation:
To find the common ratio, we pick any term but the first one and divide it over its previous term
r = common ratio
r = (second term)/(first term) = 2/4 = 1/2 = 0.5
r = (third term)/(second term) = 1/2 = 0.5
r = (fourth term)/(third term) = 0.5/1 = 0.5
Each term is cut in half to get the next one.
