2011 AMC 10A Problems/Problem 17
Problem 17
In the eight-term sequence , the value of
is 5 and the sum of any three consecutive terms is 30. What is
?
Solution
We consider the sum and use the fact that
, and hence
.
Equating the two values we get for the sum, we get the answer
.
Solution 2
We see that , and by substituting the given
, we find that
. Similarly,
and
.
Similarly, and
, giving us
. Since
,
.
Solution 3
Let . Then from
, we find that
. From
, we then get that
. Continuing this pattern, we find
,
,
, and finally
. So
Solution 4
Given that the sum of 3 consecutive terms is 30, we have
and
It follows that because
.
Subtracting, we have that .
See Also
2011 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 16 |
Followed by Problem 18 | |
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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