Geometric Sequence Game

Logic Level 2

Hans picked two consecutive positive integers.

He called the smaller number the first term and the other, the second term.
He multiplied them and called the product the third term.
He multiplied the second term to the third term and the result would be the fourth term, and so on.

Hans' sixth term is $30233088$ . Add Hans' first, second, and fifth terms.

1 solution

Arindam Ghosh
Nov 14, 2020

Denoting nth term as $a_n$

$a_1 × a_2 = a_3 = a_1 × a_2$

$a_2 × a_3 = a_4 = a_1 × a_2^2$

$a_3 × a_4 = a_5 = a_1^2 × a_2^3$

$a_4 × a_5 = a_6 = a_1^3 × a_2^5$

$a_6 = 30233088 = 2^9 × 9^5 = 8^3 × 9^5$

So $a_1 = 8$ $a_2 = 9$

$a_5 = 8^2 × 9^3 = 46656$

Ans = $a_1 + a_2 + a_5$

= 8 + 9 + 46656 = $\boxed{46673}$