Question
Real Tutor Solution
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Answer
The
th terms are:
a)
b)
c)
d)
a)
b)
c)
d)
Solution
Let’s determine the
th term for each of the given sequences:
a)
Pattern Analysis:
- This is a geometric sequence where each term is multiplied by
to get the next term. - The first term (
) is . - The common ratio (
) is .
b)
Pattern Analysis:
- This is also a geometric sequence but with each term multiplied by
to get the next term. - The first term (
) is . - The common ratio (
) is .
c)
Pattern Analysis:
- Observe the relationship between consecutive terms:
-
- Each subsequent term involves multiplying by an additional
.
Alternatively, since
, it can also be expressed as:
d)
Pattern Analysis:
- Simplify the terms:
-
can be written as . -
. -
.
-
- This suggests that each term is
.
Summary of
th Terms:
a.
a.
b.
c.
d.
Reviewed and approved by the UpStudy tutoring team
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Extra Insights
For the first series
: This is a geometric series where the first term is
and the common ratio is
. The
th term can be found using the formula
, resulting in
.
For the second series
: Similar to the first, this is also a geometric series but in this case, the first term is
with a common ratio of
. Thus, the
th term is
.
Now, isn’t math fascinating? The rules of sequences and series help us predict patterns in otherwise chaotic arrangements!