Find the 12th term of the sequence-1/3,-5/6,-4/3,-11/6
express all fractions with a denominator of 6, and it becomes quite clear. Just look at the numerators.
To find the 12th term of the given sequence, we need to first identify the pattern.
From -1/3 to -5/6, we can see that the numerator is increasing by 4 (0 - 4 = -4).
From -5/6 to -4/3, we can observe that the denominator is increasing by 3 (6 + 3 = 9).
Therefore, we can conclude that the numerator follows an arithmetic sequence decreasing by 4 each time and the denominator follows an arithmetic sequence increasing by 3 each time.
To find the 12th term, we can use the formula for the nth term of an arithmetic sequence:
nth term = first term + (n - 1) * common difference
The first term is -1/3, and the common difference for the numerator is -4. So, for the numerator, we have:
n = 12
First term = -1/3
Common difference = -4
numerator = -1/3 + (12 - 1) * (-4)
numerator = -1/3 + (11) * (-4)
numerator = -1/3 - 44
numerator = -45/3
numerator = -15
Now, let's find the denominator:
n = 12
First term = 6
Common difference = 3
denominator = 6 + (12 - 1) * 3
denominator = 6 + (11) * 3
denominator = 6 + 33
denominator = 39
Therefore, the 12th term of the given sequence is -15/39.
To find the 12th term of the sequence -1/3, -5/6, -4/3, -11/6, we need to determine the pattern in the sequence and then apply it to find the desired term.
Looking at the sequence, we can observe that the numerators alternate between -1 and -4, while the denominators alternate between 3 and 6. We can denote this pattern as follows:
Numerator: -1, -4, -1, -4, ...
Denominator: 3, 6, 3, 6, ...
To find the 12th term, we need to determine which pair of numerator and denominator to use. We know that the numerator should be -1 if the term number is even and -4 if the term number is odd. Similarly, the denominator should be 3 if the term number is even and 6 if the term number is odd.
Let's consider the term number 12. Since 12 is an even number, the numerator will be -1, and the denominator will be 3. Therefore, the 12th term can be obtained by placing -1 over 3: -1/3.
Hence, the 12th term of the sequence is -1/3.