Answer:
To find the 9th term of a geometric sequence, we can use the formula:
an = a1 * r^(n-1)
where:
an = the nth term of the sequence
a1 = the first term of the sequence
r = the common ratio of the sequence
n = the term number we want to find
In this case, we are given that the common ratio is 2/3, the first term is 6, and we want to find the 9th term. So we can plug in those values and get:
a9 = 6 * (2/3)^(9-1)
Simplifying the exponent, we get:
a9 = 6 * (2/3)^8
Using a calculator, we can evaluate the exponent:
a9 = 6 * 0.015625
Multiplying, we get:
a9 = 0.09375
Therefore, the 9th term of the geometric sequence is 0.09375.
Explanation:
here's a step-by-step explanation:
We are given the first term of the geometric sequence, a1 = 6, and the common ratio, r = 2/3. We need to find the 9th term, which we can do using the formula:
an = a1 * r^(n-1)
where n is the term number we want to find.
Step 1: Substitute the given values into the formula
a9 = 6 * (2/3)^(9-1)
Step 2: Simplify the exponent
a9 = 6 * (2/3)^8
The exponent 9-1 simplifies to 8.
Step 3: Evaluate the exponent
a9 = 6 * 0.015625
We can use a calculator to evaluate (2/3)^8, which is 0.015625.
Step 4: Multiply to find the 9th term
a9 = 0.09375
Multiplying 6 by 0.015625 gives us the 9th term of the geometric sequence, which is 0.09375.
Therefore, the 9th term of the geometric sequence whose common ratio is 2/3 and whose first term is 6 is 0.09375.