2009 AMC 12A Problem 7

Problem 7 of 25EasierAlgebra

The first three terms of an arithmetic sequence are

2x - 3,

5x - 11,

and

3x + 1

respectively. The

n

th term of the sequence is

2009.

What is

n?

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Solution

Equal consecutive differences give

(5x - 11) - (2x - 3)

= (3x + 1) - (5x - 11),

that is

3x - 8 = -2x + 12,

x = 4.

The first three terms are

5, 9, 13,

with common difference

4.

The

n

th term satisfies

2009 = 5 + (n - 1)\cdot 4,

n - 1 = 501

and

n = 502.

Thus, the correct answer is B.

Tagged: arithmetic sequence