SOLUTION: 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.

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(52832) (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,..
-------------------------------------------------------

B) and E)
=======================================================

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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