a. what is the general term of the following series?
60/121-30/11+15-... +219 615/16
b. how many terms does the series have
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a. To find the general term of the series, we need to observe the pattern in the terms.
The given series does not have a clear pattern that can be expressed in a single equation. However, we can still find the general term by analyzing the terms.
The terms of the series are:
60/121, -30/11, 15, ...
We can see that the first term is 60/121, the second term is obtained by multiplying the previous term by -1 and dividing by 4:
(-30/11) = (60/121) * (-1/4),
the third term is obtained by multiplying the previous term by -1 and dividing by 2:
(15) = (-30/11) * (-1/2),
and so on.
Thus, we can write the general term as:
an = (an-1 * (-1)^(n+1)) / (2^ceil(n/2)), where a1 = 60/121, n represents the position of the term in the series, and ceil() is the ceiling function that rounds up to the nearest integer.
b. To determine the number of terms in the series, we need to count the number of terms given.
From the given series, we have:
60/121, -30/11, 15, ..., 219 615/16
Counting them, we see that there are 24 terms in the series.