in a sequence of numbers
a3 = o,a4=4,a5=8,a6=12 and a7 =16
based on this imfromation which equaution can be used to find the nth term in the sequence, a n?
Based on the given information, we can determine that it is an arithmetic sequence with a common difference of 4.
Therefore, the equation to find the nth term (an) in the sequence can be expressed as:
an = a1 + (n-1)d
where:
an represents the nth term
a1 represents the first term in the sequence (a3 = o, implies a1 = -8)
d represents the common difference (d = 4)
Thus, the equation becomes:
an = -8 + 4(n - 1)
a_{n}=-12n+4
a_{n}=12n+4
a_{n}=4n-12
a_{n}=-4n+12
None of the provided equations match the given sequence. The correct equation for finding the nth term in the sequence based on the given information is:
an = 4n - 12
To find the equation that can be used to find the nth term in the sequence, we need to analyze the pattern in the given sequence of numbers:
a3 = o, a4 = 4, a5 = 8, a6 = 12, a7 = 16
Upon observation, we can see that the sequence is an arithmetic sequence, where each term is obtained by adding a constant difference to the previous term.
Let's analyze the differences between consecutive terms:
a4 - a3 = 4 - 0 = 4
a5 - a4 = 8 - 4 = 4
a6 - a5 = 12 - 8 = 4
a7 - a6 = 16 - 12 = 4
We can observe that the constant difference between consecutive terms is 4. This indicates that the sequence is increasing with a common difference of 4.
Now, to find the equation to determine the nth term, we can start by expressing the general form of an arithmetic sequence as:
a_n = a + (n - 1)d
Where:
a_n represents the nth term in the sequence,
a represents the first term in the sequence,
n represents the position of the term in the sequence, and
d represents the common difference between consecutive terms.
By substituting the given information, we have:
a = 0 (since a3 = 0)
d = 4 (since the common difference between terms is 4)
Therefore, the equation to find the nth term in this arithmetic sequence is:
a_n = 0 + (n - 1)4
a_n = 4n - 4
So, the equation to find the nth term in the sequence is a_n = 4n - 4.