Difference between revisions of "2015 AMC 10A Problems/Problem 7"
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==Solution 4== | ==Solution 4== | ||
Minus each of the terms by 12 to make the the sequence 1,4,7,....,61. | Minus each of the terms by 12 to make the the sequence 1,4,7,....,61. | ||
− | 61-1/3=20 | + | 61-1/3=20 20+1=21 |
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==See Also== | ==See Also== | ||
{{AMC10 box|year=2015|ab=A|num-b=6|num-a=8}} | {{AMC10 box|year=2015|ab=A|num-b=6|num-a=8}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 00:21, 14 February 2017
Problem
How many terms are in the arithmetic sequence , , , , , ?
Solution
, 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, one more must be added to include the first term. So, the answer is .
Solution 2
.
Solution 3
Using the formula for arithmetic sequence's nth term, we see that
.
Solution 4
Minus each of the terms by 12 to make the the sequence 1,4,7,....,61. 61-1/3=20 20+1=21
See Also
2015 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
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 AMC 10 Problems and Solutions |
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