2008 AMC 12A Problems/Problem 16
Problem
The numbers ,
, and
are the first three terms of an arithmetic sequence, and the
term of the sequence is
. What is
?
Solutions
Solution 1
Let and
.
The first three terms of the arithmetic sequence are ,
, and
, and the
term is
.
Thus, .
Since the first three terms in the sequence are ,
, and
, the
th term is
.
Thus the term is
.
Solution 2
If ,
, and
are in arithmetic progression, then
,
, and
are in geometric progression. Therefore,
Therefore, ,
, therefore the 12th term in the sequence is
Solution 3
See Also
2008 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 15 |
Followed by Problem 17 |
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 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.