Write the arithmetic sequence that has four arithmetic means between -20 and 20.
that is the common difference, yes.
Use it to fill in the missing four terms.
-20 and 20 are 40 apart
divide that 40 into 5 equal parts
start adding at -20 ...
40/5= 8 so it would be 8?
it would be -12,-4,4,12?
To write an arithmetic sequence with four arithmetic means between -20 and 20, we need to find the common difference (d) first.
In an arithmetic sequence, the nth term (aₙ) is given by the formula aₙ = a₁ + (n - 1)d, where a₁ is the first term and n is the position of the term.
Let's first find the number of terms, including the initial and final terms. This can be done by subtracting the initial term from the final term and adding 1.
Number of terms = (final term - initial term) + 1
= (20 - (-20)) + 1
= 41
Now, we have a total of 41 terms (including the initial and final terms). Since we want four arithmetic means between the initial and final terms, we need to divide the entire sequence into 41 - 6 = 35 segments.
To find the common difference, we divide the difference between the final and initial terms by the number of segments.
Common difference (d) = (final term - initial term) / number of segments
= (20 - (-20)) / 35
= 40 / 35
= 8/7
Now that we have the common difference, we can write the arithmetic sequence.
The first term (a₁) is -20, so we substitute the values into the equation:
aₙ = a₁ + (n - 1)d
aₙ = -20 + (n - 1)(8/7)
Therefore, the arithmetic sequence with four arithmetic means between -20 and 20 can be written as:
-20, -12 5/7, -5 6/7, 1/7, 7/7, 13/7, ..., 19 1/7, 20