Use your imagination to find the nth term 1/2,1/4,1/8,1/16
To find the nth term of the given sequence 1/2, 1/4, 1/8, 1/16, we can look for a pattern.
First, let's observe the denominators of the sequence: 2, 4, 8, 16. Notice that these are powers of 2.
Let's rewrite the sequence using the powers of 2:
1/2 = 2^-1
1/4 = 2^-2
1/8 = 2^-3
1/16 = 2^-4
From the pattern, we can conclude that the nth term is given by 2^(-n).
So, the nth term of the sequence is 2^(-n).
If we observe the given sequence, we can see that each term is obtained by dividing the previous term by 2.
The first term is 1/2.
The second term is 1/2 ÷ 2 = 1/4.
The third term is 1/4 ÷ 2 = 1/8.
The fourth term is 1/8 ÷ 2 = 1/16.
This pattern continues, dividing each term by 2 to obtain the next term.
Therefore, the nth term, denoted by Tn, can be calculated as:
Tn = 1/(2^n)
For example:
T1 = 1/(2^1) = 1/2
T2 = 1/(2^2) = 1/4
T3 = 1/(2^3) = 1/8
T4 = 1/(2^4) = 1/16
Using this formula, we can find the nth term for any position in the sequence.
To find the nth term of the given sequence, we need to observe the pattern and determine the relationship between the terms. Let's take a look at the sequence:
1/2, 1/4, 1/8, 1/16
By examining the sequence, we can see that each term is half the value of the previous term. So, to obtain the nth term, we can use the formula:
nth term = first term * common ratio^(n-1)
In this case, the first term is 1/2, and the common ratio is 1/2 (since each term is half the value of the previous term). So, let's substitute these values into the formula:
nth term = (1/2) * (1/2)^(n-1)
Simplifying further:
nth term = 1/2^n
Therefore, the nth term of the given sequence is 1/2^n.