20th term = common ratio raised to the power of 19.
To find the 20th term of a geometric sequence, we need to know the first term and the common ratio. The first term is given as 1, but we don't know the common ratio. We can find the common ratio by dividing any term by the previous term. For example, if we divide the second term by the first term, we get the common ratio.
a2 / a1 = common ratio
We don't know the second term, but we can rewrite it as the first term multiplied by the common ratio.
a2 = a1 * common ratio
Substituting this into our equation, we get:`
(a1 * common ratio) / a1 = common ratio
Canceling the a1 terms, we are left with the common ratio.
common ratio = common ratio
This is a tautology, which means that it is always true. Therefore, any number can be the common ratio of a geometric sequence.
To find the 20th term of the geometric sequence, we can use the following formula:
an = a1 * r^(n - 1)
where:
an is the nth term of the sequence
a1 is the first term of the sequence
r is the common ratio of the sequence
n is the number of terms in the sequence
Substituting the known values, we get:
a20 = 1 * r^(20 - 1)
a20 = r^19
Since we don't know the common ratio, we can't find the exact value of the 20th term. However, we can say that the 20th term is equal to the common ratio raised to the power of 19.