Answer:
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1 answer:
Answer:
The answer is A. 31,250.
Step-by-step explanation:
To solve for the 7th term in the geometric sequence, start by plugging 7 into the explicit formula, and the formula will look like .
Next, subtract 1 from 7, and the formula will look like .
Then, raise 5 to the power of 6, which will look like .
Finally, multiply 2 by 15,625, and the answer will be 31,250.
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If 
is odd, then
while if is even, then the sum would be
The latter case is easier to solve:
which means
.
In the odd case, instead of considering the above equation we can consider the partial sums. If is odd, then the sum of the even integers between 1 and would be
Now consider the partial sum up to the second-to-last term,
Subtracting this from the previous partial sum, we have
We're given that the sums must add to
, which means
But taking the differences now yields
and there is only one for which 
; namely, 
. However, the sum of the even integers between 1 and 5 is 
, whereas 
. So there are no solutions to this over the odd integers.
while if
The latter case is easier to solve:
which means
In the odd case, instead of considering the above equation we can consider the partial sums. If
Now consider the partial sum up to the second-to-last term,
Subtracting this from the previous partial sum, we have
We're given that the sums must add to
But taking the differences now yields
and there is only one