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United States competition problems

Algebra Difficulty 4.0 AIME Find the answer United States

Problem:

For the sequence of numbers $n_{1}, n_{2}, n_{3}, \ldots$ , the relation $n_{i}=2 n_{i-1}+a$ holds for all $i>1$ . If $n_{2}=5$ and $n_{8}=257$ , what is $n_{5}$ ?

Your answer

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

Solution

Solution:

33 .

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