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The 1st term in the geometric sequence below is −13. If it can be (April 2021 - D05)
The 1st term in the geometric sequence below is −13. If it can be determined, what is the 6th term?
−13, 26, −52, 104, −208, …
A. −416
B. −312
C. 312
D. 416
E. Cannot be determined from the given information
Solution
Correct answer: D. 416.
To find the 6th term in the geometric sequence, we need to identify the common ratio r first. We can find the common ratio by dividing any term by its preceding term.
Common ratio r = Any term / Preciding term
Let's take the ratio of the second term to the first term:
r = 26/-13 = -2
Now that we have the common ratio r = −2, we can find the 6th term using the formula for the nth term of a geometric sequence:
Given 𝑎1 = −13 and r = −2, we can find the 6th term (𝑎6):
Exam Edition: April 2021 - D05
Exam Year: 2021
Related topics: Geometric Sequence Problem