Answer:
- (d) 2 +(-5) +(-12) +...
- (a) a8
Step-by-step explanation:
1.
Putting n = 0 and n = 1 into the expression being summed will show you which series is correct.
2 -7n for n=0 is 2 -7·0 = 2
2 -7n for n=1 is 2 -7·1 = -5
The series of the last choice (d) is correct.
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2.
The given sequence is exponential with a first term of 3 and a common ratio if -5. Then the n-th term is ...
an = 3(-5)^(n -1)
We want to find n for an = -234,375.
-234375 = 3(-5)^(n-1)
-78125 = (-5)^(n-1)
For n to be a real number, we must have n even. In that case, the value of n is equivalent to the value that is the solution to ...
78125 = 5^(n -1)
Taking logs of both sides, we get ...
log(78125) = (n -1)·log(5)
log(78125)/log(5) = n -1 . . . . . . . . . . . . divide by log(5)
n = 1 +log(78125)/log(5) = 1 +7 = 8 . . . add 1 and evaluate
-234,375 is the 8th term of the sequence.
