The explicit function is (b) f(n) = -4(n - 1) + 3; the seventh term is -21
How to determine the explicit form?
The given parameters are:
- First term of the sequence, a = 3
- Common difference of the sequence, d = -4
The explicit form is for an arithmetic function.
An arithmetic function has an explicit form represented as:
f(n) = a + (n -1) * d
Substitute the values of n and a in the above equation
f(n) = 3 + (n -1) * -4
Evaluate the product i.e. multiply -4 by (n - 1)
f(n) = 3 -4(n - 1)
Rewrite the equation as
f(n) = -4(n - 1) + 3
The seventh term is then calculated as:
f(n) = -4(n - 1) + 3
Substitute 7 for n in the above equation
f(7) = -4(7 - 1) + 3
Evaluate
f(7) = -21
Hence, the explicit function is (b) f(n) = -4(n - 1) + 3; the seventh term is -21
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