Find the 11th term of a geometric sequence if a1 = 45 (first term) and the common ratio r = 0.2.
A simple application of your formula ...
term(n) = a r^(n-1)
term(11) = 45 (.2)^10
= 45(.0000001024) = 0.000004608
or as an exact fraction:
term(11) = 45(1/5)^10
= 45/9765625
= 9/1953125
Well, if the first term is 45 and the common ratio is 0.2, then to find the 11th term, I'm going to need a little mathematical assistance. Let's do some calculations!
The general formula for the nth term of a geometric sequence is given by:
an = a1 * r^(n-1)
Substituting in the given values, we have:
a11 = 45 * 0.2^(11-1)
Simplifying:
a11 = 45 * 0.2^10
Now, let's calculate:
a11 = 45 * 0.0000001024
Drumroll, please...
And the 11th term of the geometric sequence is...
wait for it...
approximately 0.000004608!
Hope that answer was worth the wait! 🎉
To find the 11th term of a geometric sequence, we can use the formula:
an = a1 * r^(n-1)
Given the values:
a1 = 45 (first term)
r = 0.2 (common ratio)
n = 11 (term we want to find)
We can substitute these values into the formula to find the 11th term:
a11 = 45 * 0.2^(11-1)
= 45 * 0.2^10
To simplify the calculation, let's calculate 0.2^10 separately first:
0.2^10 = 0.2 * 0.2 * 0.2 * 0.2 * 0.2 * 0.2 * 0.2 * 0.2 * 0.2 * 0.2
= 0.0000001024
Now, substitute the value back into the equation:
a11 = 45 * 0.0000001024
≈ 0.000004608
Therefore, the 11th term of the geometric sequence is approximately 0.000004608.
To find the 11th term of a geometric sequence, we can use the formula:
an = a1 * r^(n-1),
where an is the nth term, a1 is the first term, r is the common ratio, and n is the position of the term.
In this case, a1 = 45, r = 0.2, and we need to find the 11th term.
Using the formula, we substitute the given values into the equation:
a11 = 45 * (0.2)^(11-1).
First, calculate the exponent part:
(0.2)^(11-1) = (0.2)^10.
To evaluate this, we can either use a calculator or perform exponentiation step by step.
Using a calculator, we get:
(0.2)^10 ≈ 0.0000001024.
Therefore, the 11th term of the geometric sequence is:
a11 = 45 * 0.0000001024 ≈ 0.000004608.
Hence, the 11th term of the geometric sequence is approximately 0.000004608.