Question
Question 6
For the series
, find:
(i) the first term and the common ratio
(ii) the sum of the first 6 terms
For the series
(i) the first term and the common ratio
(ii) the sum of the first 6 terms
Ask by Fitzgerald Bright. in Australia
Jan 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
First term: 27
Common ratio: -1/3
Sum of the first 6 terms: 20.222
Common ratio: -1/3
Sum of the first 6 terms: 20.222
Solution

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Extra Insights
The first term in the series
is
, and the common ratio can be found by dividing the second term by the first term:
. So, we have a first term of
and a common ratio of
.
To find the sum of the first 6 terms of the geometric series, you can use the formula for the sum of the first
terms:
Plugging in the values:
The calculation goes:
Calculating
, we have:
So, the sum of the first 6 terms is approximately
.