What is the 11th term of the geometric sequence
3, 6, 12, 24, …
To find the 11th term of the geometric sequence, we can use the formula for the nth term of a geometric sequence:
an = a1 * r^(n-1)
where an represents the nth term, a1 is the first term, r is the common ratio, and n is the position of the term in the sequence.
In this case, the first term is 3, and the common ratio can be found by dividing any term by the previous term. Let's calculate it:
r = 6/3 = 2
Now we can plug in the values into the formula to find the 11th term:
a11 = 3 * 2^(11-1)
= 3 * 2^10
= 3 * 1024
= 3072
So, the 11th term of the geometric sequence is 3072.
To find the 11th term of a geometric sequence, we need to know the first term and the common ratio.
In this sequence, the first term (a) is 3, and we can find the common ratio (r) by dividing any term by its previous term. Let's calculate:
Common ratio (r) = 6 / 3 = 2
Now that we have the first term (a = 3) and the common ratio (r = 2), we can use the formula for finding the nth term of a geometric sequence:
nth term = a * (r^(n-1))
Plugging in the values, we get:
11th term = 3 * (2^(11-1))
Simplifying further:
11th term = 3 * 2^10
11th term = 3 * 1024
11th term = 3072
Therefore, the 11th term of the given geometric sequence is 3072.
To find the 11th term of a geometric sequence, we first need to determine the common ratio (r) of the sequence.
In this case, let's look at the pattern between consecutive terms. We can see that each term is obtained by multiplying the previous term by 2.
So, the common ratio (r) is 2.
The formula to find the nth term of a geometric sequence is:
term(n) = a * (r^(n-1)).
Here, a represents the first term of the sequence, and n represents the position of the term we want to find.
In this given sequence, the first term (a) is 3. And we want to find the 11th term, which corresponds to n = 11.
So, the formula becomes:
term(11) = 3 * (2^(11 - 1))
term(11) = 3 * (2^10)
term(11) = 3 * 1024
term(11) = 3072
Therefore, the 11th term of the given geometric sequence is 3072.