Answer
18, 9, 0
Step-by-step explanation:
The formula to get the arithmetic means is:
[tex]a_n = a_1 + (n + 1)d[/tex]
where [tex]a_n[/tex] is the nth term you want to find,
[tex]a_1[/tex] is the first term
[tex]n\\[/tex] is the number of terms, and
[tex]d[/tex] is the common difference
[tex]a_n = a_1 + (n - 1)d[/tex]
[tex]n = 5, a_1 = 27, d = ?[/tex]
Substitute
[tex]-9 = 27 + (5 - 1)d[/tex]
Follow PEMDAS (Parentheses, Exponent, Multiplication, Division, Additoin, Subtraction)
[tex]-9 = 27 + (4)d\\\\-9 = 27 + 4d[/tex]
Subtract 27 from both sides
[tex]-27 - 9 = 4d\\\\-36 = 4d[/tex]
Divide both sides by 4:
[tex]\frac{-36}{4} = \frac{4d}{4}\\\\-9 = d[/tex]
You can use the recursive formula:
[tex]a_n = a_{n - 1} - 9[/tex]
which when used to [tex]a_2, a_3,[/tex] and [tex]a_4[/tex], you get:
[tex]27,18,9,0,-9[/tex]
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Verified answer
Answer
18, 9, 0
Step-by-step explanation:
Arithmetic Means
Formula
The formula to get the arithmetic means is:
[tex]a_n = a_1 + (n + 1)d[/tex]
where [tex]a_n[/tex] is the nth term you want to find,
[tex]a_1[/tex] is the first term
[tex]n\\[/tex] is the number of terms, and
[tex]d[/tex] is the common difference
Get the common difference
[tex]a_n = a_1 + (n - 1)d[/tex]
[tex]n = 5, a_1 = 27, d = ?[/tex]
Substitute
[tex]-9 = 27 + (5 - 1)d[/tex]
Follow PEMDAS (Parentheses, Exponent, Multiplication, Division, Additoin, Subtraction)
[tex]-9 = 27 + (4)d\\\\-9 = 27 + 4d[/tex]
Subtract 27 from both sides
[tex]-27 - 9 = 4d\\\\-36 = 4d[/tex]
Divide both sides by 4:
[tex]\frac{-36}{4} = \frac{4d}{4}\\\\-9 = d[/tex]
Get the 2nd, 3rd and 4th term
You can use the recursive formula:
[tex]a_n = a_{n - 1} - 9[/tex]
which when used to [tex]a_2, a_3,[/tex] and [tex]a_4[/tex], you get:
[tex]27,18,9,0,-9[/tex]