2015 AMC 10A Problems/Problem 7
Contents
Problem
How many terms are in the arithmetic sequence , , , , , ?
Solution 1
, so the amount of terms in the sequence , , , , , is the same as in the sequence , , , , , .
In this sequence, the terms are the multiples of going up to , and there are multiples of in .
However, the number 0 must also be included, adding another multiple. So, the answer is .
Solution 2
Using the formula for arithmetic sequence's nth term, we see that .
Solution 3
Minus each of the terms by to make the the sequence .
.
Solution 4
Subtract each of the terms by to make the sequence . Then divide the each term in the sequence by to get . Now it is clear to see that there are terms in the sequence. .
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See Also
2015 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
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All AMC 10 Problems and Solutions |
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