Berkeley Math Circle

Algebra Difficulty 4.0 AIME Find the answer United States

Problem:

In the sequence
$1, 4, 7, 10, 13, 16, 19, \ldots$
each term is 3 less than the next term. Find the 1000th term of the sequence.

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Solution:

To get from the first term to the 1000th term, we must add three 999 times. That amounts to adding $3 \cdot 999$ which is $2997$ . So the 1000th term is $1 + 2997 = 2998$ .

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.