HMMT February

Algebra Difficulty 4.8 AIME Find the answer

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

33.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.