Question
LCTIVITIESIASSESSMENTS
L. 2 Calculate the sum of the first 12 terms of the geometric sequence
;
L 3 Calculate
L. 4 Determine
if:
L. 5 What is the least value of
for which the series
?
L. 2 Calculate the sum of the first 12 terms of the geometric sequence
L 3 Calculate
L. 4 Determine
L. 5 What is the least value of
Ask by Bernard Ellis. in South Africa
Jan 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Solutions:
-
L.2: The sum of the first 12 terms is -341.25.
-
L.3: The sum is 31.9375 or
. -
L.4: The value of
is 6. -
L.5: The least value of
is 10.
Solution

Sign in to Unlock Answers for Free!
A Learning Platform Trusted by Millions of Real Students and Teachers.

Answered by UpStudy AI and reviewed by a Professional Tutor
Like
The Deep Dive
The concept of a geometric sequence dates back to ancient civilizations like the Babylonians and Greeks, who recognized the pattern in taking a fixed ratio between terms. For instance, in your sequence, the common ratio is
, which leads to exciting patterns and relationships in mathematics. By summing the first 12 terms, you not only get a taste of this mathematical elegance but also glimpse how these sequences relate to exponential functions!
If you’re tackling these tasks, a handy tip is to remember that geometric series can often be simplified using the formula
. However, make sure to pay close attention to sign and value changes in your series, particularly with negative ratios! Miscalculating the signs or forgetting to adjust for the first term can lead to a wild goose chase through your math!