Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 4.8 AIME Find the answer

Lake 1. Given the arithmetic sequence with the first term $a_{1}=3, a_{n+1}=a_{n}+5$ , find up to the 5th term.

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

Solution: From the recursive formula $a_{2}=a_{1}+5=3+5=8$ ,
$\begin{array}{l} a_{3}=a_{2}+5=8+5=13, \\ a_{4}=a_{3}+5=13+5=18, \\ a_{5}=a_{4}+5=18+5=23 . \end{array}$

From the recursive formula to find the general term, there are commonly four forms:
I $\cdot a_{n+1}=a_{n}+d$ ,
Arithmetic sequence type.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.