Question
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  1. Calculate the value of the th term.
    a
    b
    c
    (d)

Ask by Kirk Warner. in South Africa
Jan 29,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

The th terms are:
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 .
th Term:

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 .
th Term:

c)

Pattern Analysis:
  • Observe the relationship between consecutive terms:
  • Each subsequent term involves multiplying by an additional .
th Term:
Alternatively, since , it can also be expressed as:

d)

Pattern Analysis:
  • Simplify the terms:
    • can be written as .
    • .
    • .
  • This suggests that each term is .
th Term:

Summary of th Terms:
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!

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