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2013 HMMT Algebra #2: Arithmetic and Geometric Series

Source:

February 16, 2013

HMMTarithmetic sequencegeometric sequence

Problem Statement

Let

\{a_n\}_{n\geq 1}

be an arithmetic sequence and

\{g_n\}_{n\geq 1}

be a geometric sequence such that the first four terms of

\{a_n+g_n\}

are

0

0

1

, and

0

, in that order. What is the

10

th term of

\{a_n+g_n\}