Question
The second term of a geometric sequence is 6 and the fourth term is 5
Find the sums of two possible series to 20 terms.
Find the sums of two possible series to 20 terms.
Ask by Beck Stanley. in South Africa
Jan 27,2025
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Tutor-Verified Answer
Answer
The sums of the two possible 20-term geometric series are approximately 63.4 and –2.88.
Solution

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Mind Expander
To solve the problem, we first notice that in a geometric sequence, each term can be represented as
, where
is the first term and
is the common ratio. Given the second term is 6, we have
, and for the fourth term being 5, we have
.
By dividing the equations, we can find
:
Using
values, we can find
. For
:
gives
.
For
:
gives
.
Now we have two possible series. The sum
of the first
terms of a geometric series is given by:
Calculating
:
-
For
: -
For
:
Both calculations will yield the sums for the two possible series to 20 terms.