Question
- The sum of the lirst 5 ferms of an arithmetic sequence is 0 and the fifth term is 8 . Determin
contmond diference and the first term.
- In a geonetific series the first term is 36 , the last term is 16 and the sum of the series is 76 .
Determine the coinmon ratio and the number of terns in the sequence.
contmond diference and the first term.
Determine the coinmon ratio and the number of terns in the sequence.
Ask by Medina Barber. in South Africa
Jan 05,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Problem 4:
- First term (
): - Common difference (
):
Problem 5:
- Common ratio (
): - Number of terms (
):
Solution

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Beyond the Answer
In an arithmetic sequence, if the sum of the first five terms is zero and the fifth term is 8, you can set up some equations. The fifth term is given by
(where
is the first term and
is the common difference). The sum of the first five terms can be expressed as
. Solving this system of equations gives you the values for
and
as
and
respectively.
For the geometric series where the first term is 36, the last term is 16, and the sum of the series is 76, you can use the formula for the sum of a geometric series
. Here, you can set up equations involving
,
, and
to solve for the common ratio
and the number of terms
. After some manipulations, you find
is approximately
and
is 5.