1988 AJHSME Problems/Problem 19

Problem

What is the $100\text{th}$ number in the arithmetic sequence: $1,5,9,13,17,21,25,...$ ?

$\text{(A)}\ 397 \qquad \text{(B)}\ 399 \qquad \text{(C)}\ 401 \qquad \text{(D)}\ 403 \qquad \text{(E)}\ 405$

Solution

To get from the $1^\text{st}$ term of an arithmetic sequence to the $100^\text{th}$ term, we must add the common difference $99$ times. The first term is $1$ and the common difference is $5-1=9-5=13-9=\cdots = 4$ , so the $100^\text{th}$ term is $1+4(99)=397 \rightarrow \boxed{\text{A}}$

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1988 AJHSME Problems/Problem 19

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Solution

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