Tell whether the sequence is arithmetic. If it is, write a function rule to represent it.
0.2, -0.6, -1.4, -2.2
This is an arithmetic sequence, but I do not understand the function rule of A(n) = 0.2 - 0.8(n-1), which is the given answer.
note that each term is 0.8 less than the previous. That means that the formula will look like
A(n) = -0.8n
But, we need A(1) = 0.2
0.2 = -.8 + 1, so
A(n) = 1 - 0.8n
But, most people like n=0 for the first term A(1), so we need to adjust for that, giving the formula above.
what is 996587*968547*6584/85
no idea. get out your calculator, or just type it into google.
To determine if the given sequence is arithmetic, we need to check if there is a common difference between consecutive terms.
In this case, we can find the common difference by subtracting any term from the next term. Let's check:
-0.6 - 0.2 = -0.8
-1.4 - (-0.6) = -0.8
-2.2 - (-1.4) = -0.8
As we can see, there is a common difference of -0.8. Therefore, the sequence is arithmetic.
Now, let's find the function rule for this arithmetic sequence. A function rule represents a numerical pattern in terms of an unknown variable, usually denoted by 'n' in this case.
To find the function rule, we need to identify the initial term and the common difference.
In this case, the initial term is 0.2 and the common difference is -0.8.
The general formula for an arithmetic sequence is:
A(n) = a + (n - 1)d
where a is the initial term, n is the position of the term in the sequence, and d is the common difference.
So, plugging in the values:
A(n) = 0.2 + (n - 1)(-0.8)
Expanding and simplifying:
A(n) = 0.2 - 0.8(n - 1)
This is the function rule that represents the arithmetic sequence.