Math Gold Medalist

Lor

2023 AMC 8 

Problem 22

In a sequence of positive integers, each term after the second is the product of the previous two terms. The sixth term is $4000$. What is the first term?

$\textbf{(A)}\ 1 \qquad \textbf{(B)}\ 2 \qquad \textbf{(C)}\ 4 \qquad \textbf{(D)}\ 5 \qquad \textbf{(E)}\ 10$

Prime Factorization

a , b , ab , a*b^2 , a^2*b^3, a^3*b^5 = 4000

Prime Factorize 4000

Consider cases of b 

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   Solution