Question
If the first 5 terms of a geometric sequence are
, then the
formula for the
term in the sequence is
formula for the
Ask by Coleman Ramirez. in the United States
Jan 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The
term of the sequence is
.
Solution
A geometric sequence is defined by its first term
and a common ratio
such that each subsequent term is obtained by multiplying the previous term by
.
Given the first five terms of the sequence:
-
Identify the first term (
): -
Determine the common ratio (
): To confirm, check subsequent terms:So,is consistent. -
Formulate the
term:
The general formula for theterm of a geometric sequence is: Substituting the known values:
Final Formula:
Answer: After simplifying, the nth term is 12 multiplied by (½)ⁿ⁻¹. Thus,
aₙ = 12 · (1/2)^(n−1)
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Bonus Knowledge
In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio. In this case, the common ratio
can be found by dividing any term by the previous term. For example,
. This means each term is half of the previous one!
To formulate the
term, we can express it as
. Here,
and
. Plugging in the known values, the formula becomes
.
Now you can have fun finding any term you desire in this sequence!