Find the nth term of the geometric sequence with given first term a and common ratio r.a = −6, r = −3an = What is the fourth term?a4 =
Question
Find the nth term of the geometric sequence with given first term a and common ratio r.
- a = −6
- r = −3
**an = **
What is the fourth term?
**a4 = **
Solution
The nth term of a geometric sequence can be found using the formula:
an = a * r^(n-1)
where:
- an is the nth term of the sequence,
- a is the first term of the sequence,
- r is the common ratio,
- n is the term number.
Given that a = -6 and r = -3, we can substitute these values into the formula to find the fourth term (n=4) of the sequence:
a4 = a * r^(4-1) a4 = -6 * (-3)^(4-1) a4 = -6 * (-3)^3 a4 = -6 * -27 a4 = 162
So, the fourth term of the sequence is 162.
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