Arithmetic Progression

Algebra Level 3

Let $\{a_n\}$ be an arithmetic progression with common difference $2.$ If $|a_3-1|=|a_6-3|,$ what is the smallest positive integer $k$ such that $a_k>92?$

The answer is 50.

1 solution

Aaaaaa Bbbbbb
May 2, 2014

From the common difference, $a_6=6+a_3$ From the absolute value property $a_6-3=1-a_3$ Together, these imply $a_3=-1$ and $a_6=5$ . So that $a_n = 2n-7$ .

Comparing $2n-7$ and 92, we see that we must have $n=\lceil 99/2 \rceil=50$

Arithmetic Progression

The answer is 50.

1 solution

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