Answer:
a) y = 9 -2.6(x -1)
b) -92.4
c) 18 11/13
Step-by-step explanation:
First of all, the given sequence is not an arithmetic sequence. The difference between the first two numbers is -3. The differences between successive pairs after that is -2.6.
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a) If we assume the sequence should be ...
9, 6.4, 3.8, 1.2, ...
Then the first term (a1) is 9 and the common difference (d) is -2.6. The generic term (an) is generally written as ...
an = a1 + d(n-1)
This problem seems to assume that the variables are x (term number) and y (sequence value), so the equation with the above numbers is ...
y = 9 -2.6(x -1)
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b) For x=40, the sequence term is ...
y = 9 -2.6(40 -1) = -92.4
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c) In general, it makes no sense to ask for the index number of a value that is not part of the sequence. However, we can use the formula to find a value of x that will produce the desired value of y.
-37.4 = 9 - 2.6(x -1)
-46.4 = -2.6(x -1) . . . . . subtract 9
-46.4/-2.6 = x -1 . . . . . .divide by -2.6
17 11/13 = x -1 . . . . . . . . evaluate the left side
18 11/13 = x . . . . . . . . . add 1
The desired value of x is 18 11/13.
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Comment on the question
This is a badly-formulated question that is not about arithmetic sequences at all. At best, it is about linear equations. At worst, it is a waste of the student's time, since the given data is nonsense, as is the final question in the context of an arithmetic sequence.
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Alternate answers
If you take the first term at face value and assume the common difference is supposed to b -2.6, then the answers become ...
a) y = 9.4 -2.6(x -1) . . . . or . . . . y = 12 -2.6x
b) -92
c) 19
This means the terms shown should be ... 9.4, 6.8, 4.2, 1.6
