Here's a pattern: 2, 4, 8, 16, 32.
What's the nth term?
2^n
To find the nth term of a pattern, we can analyze the given sequence and look for a common relationship between the numbers.
In this case, it appears that each number in the sequence is obtained by multiplying the previous number by 2. This means that the sequence is increasing exponentially, with a common ratio of 2.
To find the nth term, we can use the formula for a geometric sequence:
an = a1 * r^(n-1)
In this formula:
an represents the nth term,
a1 represents the first term,
r represents the common ratio, and
n represents the position of the term.
Given that the first term (a1) is 2 and the common ratio (r) is 2, we can substitute these values into the formula to find the nth term.
Therefore, the nth term of the given sequence is:
an = 2 * 2^(n-1).
For example, to find the 5th term (n=5):
a5 = 2 * 2^(5-1)
a5 = 2 * 2^4
a5 = 2 * 16
a5 = 32.
Let me know if there is anything else I can help you with.
To find the nth term of a pattern, we need to determine the rule or formula that governs the pattern. Let's analyze the given pattern:
2, 4, 8, 16, 32
If we observe carefully, we can see that each term is obtained by multiplying the previous term by 2. So, the pattern can be described as each term is obtained by doubling the previous term.
To find the nth term, we can apply this rule. Starting with the first term (2), we need to multiply it by 2 (n-1) times, where n represents the position of the term in the pattern.
Therefore, the general formula for the nth term of this pattern is:
nth term = 2 x 2^(n-1)
Now, if you want to find the value of a specific term, plug its position (n) into the formula. For example, to find the value of the 5th term, substitute n = 5 into the formula:
5th term = 2 x 2^(5-1)
= 2 x 2^4
= 2 x 16
= 32
Hence, the 5th term of the given pattern is 32. You can find the value of any term in the same way by substituting its position into the formula we derived.