Question 1003636: Which of the following sequences are arithmetic?
Select one or more:
A. 1, -2, 4, -8, 16,-32,...
B. 20, 12, 4, -4, -12, ...
C. 1, 2, 4, 7, 11, ...
D. -10, -5, 1, 8, 16,...
E. 9.3, 9.9, 10.5, 11.1, 11.7,..
How many terms of the sequence 2, 4, 6, 8, 10,... yield a sum of 132?
Answer by ikleyn(52830)   (Show Source):
You can put this solution on YOUR website! .
1) Which of the following sequences are arithmetic?
Select one or more:
A. 1, -2, 4, -8, 16,-32,...
B. 20, 12, 4, -4, -12, ...
C. 1, 2, 4, 7, 11, ...
D. -10, -5, 1, 8, 16,...
E. 9.3, 9.9, 10.5, 11.1, 11.7,..
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B) and E)
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2) How many terms of the sequence 2, 4, 6, 8, 10,. . . yield a sum of 132?
It is the arithmetic progression with the first term 2 and the common difference 2.
The formula for the sum of n first terms of an arithmetic progression is
 = 
(see the lesson Arithmetic progressions in this site).
In this case =  =  .
Therefore, to find n, we need to solve an equation
2n + n*(n-1) = 132.
Simplify and solve:
 +  -  =  ,
+ - =  ,
Factor:
(n-11)*(n+12) = 0,
The roots are n = 11 and n = -12.
Only n = 11 does suit.
Answer. n = 11.
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