Difference between revisions of "1988 AJHSME Problems/Problem 19"
5849206328x (talk | contribs) (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...) |
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==Problem== | ==Problem== | ||
| − | What is the <math>100\text{th}</math> number in the arithmetic sequence: <math>1,5,9,13,17,21,25,...</math>? | + | 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)}\ 401 \qquad \text{(D)}\ 403 \qquad \text{(E)}\ 405</math> | <math>\text{(A)}\ 397 \qquad \text{(B)}\ 399 \qquad \text{(C)}\ 401 \qquad \text{(D)}\ 403 \qquad \text{(E)}\ 405</math> | ||
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==Solution== | ==Solution== | ||
| − | To get from the <math>1^\text{st}</math> term of an arithmetic sequence to the <math>100^\text{th}</math> term, we must add the common difference <math>99</math> times. The first term is <math>1</math> and the common difference is <math>5-1=9-5=13-9=\cdots = 4</math>, so the <math>100^\text{th}</math> term is <cmath>1+4(99)=397 \rightarrow \boxed{\text{A}}</cmath> | + | To get from the <math>1^\text{st}</math> term of an arithmetic sequence to the <math>100^\text{th}</math> term, we must add the common [[difference]] <math>99</math> times. The first term is <math>1</math> and the common difference is <math>5-1=9-5=13-9=\cdots = 4</math>, so the <math>100^\text{th}</math> term is <cmath>1+4(99)=397 \rightarrow \boxed{\text{A}}</cmath> |
==See Also== | ==See Also== | ||
| − | + | {{AJHSME box|year=1988|num-b=18|num-a=20}} | |
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
Revision as of 22:26, 3 June 2009
Problem
What is the 
number in the arithmetic sequence: 
?
Solution
To get from the 
term of an arithmetic sequence to the 
term, we must add the common difference 
times. The first term is 
and the common difference is 
, so the term is ![\[1+4(99)=397 \rightarrow \boxed{\text{A}}\]](http://latex.artofproblemsolving.com/0/6/8/0682fb58e52e5fc8f72668b4c6ae80ccebbe24d1.png)
See Also
| 1988 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 18 |
Followed by Problem 20 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
