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2025 SSMO Accuracy Round Problems/Problem 1

Revision as of 11:26, 9 September 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== An infinite sequence of real numbers <math>a_1, a_2, \dots</math> satisfies <cmath>a_n = a_1+a_2+\dots+a_{n-1}</cmath> for all positive integers <math>n > 1</math...")
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Problem

An infinite sequence of real numbers $a_1, a_2, \dots$ satisfies \[a_n = a_1+a_2+\dots+a_{n-1}\] for all positive integers $n > 1$. Given that $a_{20}=25,$ find $a_{25}$.

Solution

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