2023 AMC 8 Problems/Problem 22
Problem
In a sequence of positive integers, each term after the second is the product of the previous two terms. The sixth term is . What is the first term?
Solution
Suppose the first two terms were and
. Then, the next terms would be
,
,
, and
. Since
is the sixth term, this must be equal to
. So,
. Trying out the choices, we get that
,
, which means that the answer is
~MrThinker
Solution 2
We assign A as a term in the sequence. Where a_1 = C(First Number in the Seqence)
a_6 = C^3 \cdot D^5 -> 4000$$ (Error compiling LaTeX. Unknown error_msg)
Therefore after prime factorizing 4000 as 5^3 \cdot 2^5,
We find
as our anwser
~cxrupptedpat, wuwang2002, apex304
Animated Video Solution
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