What is the 11th term of the geometric sequence
3, 6, 12, 24,
The common ratio of this geometric sequence is found by dividing any term by its preceding term.
The common ratio is 6/3 = 2.
To find the 11th term, we can use the formula for the nth term of a geometric sequence:
nth term = a * r^(n-1)
where a is the first term, r is the common ratio, and n is the desired position.
In this case, the first term is 3, the common ratio is 2, and the desired position is 11.
11th term = 3 * 2^(11-1) = 3 * 2^10 = 3 * 1024 = 3072.
Therefore, the 11th term of the sequence is 3072.
To find the 11th term of the geometric sequence, we can use the formula:
an = a1 * r^(n-1)
where:
an represents the nth term of the sequence,
a1 represents the first term of the sequence,
r represents the common ratio, and
n represents the position of the term we want to find.
In this case, a1 = 3, r = 2, and n = 11.
Plugging these values into the formula, we get:
a11 = 3 * 2^(11-1)
Simplifying further:
a11 = 3 * 2^10
Calculating:
a11 = 3 * 1024
a11 = 3072
Therefore, the 11th term of the geometric sequence 3, 6, 12, 24, ... is 3072.
To find the 11th term of the geometric sequence 3, 6, 12, 24, we can use the formula for the nth term of a geometric sequence. The formula is given by:
an = a1 * r^(n-1)
Where:
- an represents the nth term of the sequence
- a1 represents the first term of the sequence
- r represents the common ratio between consecutive terms
- n represents the position of the term we want to find
In this case, the first term (a1) is 3 and the common ratio (r) can be found by dividing any term by the previous term. In this sequence, we can see that each term is obtained by multiplying the previous term by 2. So, the common ratio (r) is 2.
Using the formula, we can substitute the given values into it to find the 11th term (a11):
a11 = 3 * 2^(11-1)
a11 = 3 * 2^10
a11 = 3 * 1024
a11 = 3072
Therefore, the 11th term of the geometric sequence 3, 6, 12, 24 is 3072.