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Question 1058766: The first term in a sequence is 2 and every term after it is -2 times the preceding term. How many of the first 100 terms are less than 100
Answer by solve_for_x(190)   (Show Source):
You can put this solution on YOUR website! The n-th term in the sequence is given by:
-(-2)^n
The first term corresponds to n = 1: -(-2)^1 = -(-2) = 2
The next five terms are:
n= 2: -4
n = 3: 8
n = 4: -16
n = 5:, 32
n = 6: -64
For the remaining terms, half will be negative and thus will be less than 100, while the other
half will be greater than 100.
The total number that are less than 100 will be:
6 + (100 - 6)/2 = 53
Solution: There will be 53 terms that are less than 100.
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