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Difference between revisions of "1988 AJHSME Problems/Problem 19"

(New page: ==Problem== What is the <math>100\text{th}</math> number in the arithmetic sequence: <math>1,5,9,13,17,21,25,...</math>? <math>\text{(A)}\ 397 \qquad \text{(B)}\ 399 \qquad \text{(C)}\ 4...)
(No difference)

Revision as of 13:13, 20 April 2009

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 \[1+4(99)=397 \rightarrow \boxed{\text{A}}\]

See Also

1988 AJHSME Problems

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