Respuesta :
Answer: 2560
Work Shown
Plug n = 2 into the formula. This is so we determine the second term.
f(n) = -4*f(n-1)
f(2) = -4*f(2-1)
f(2) = -4*f(1)
f(2) = -4*10
f(2) = -40
The short version of this is basically "multiply the first term by -4 to get the second term".
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Repeat for n = 3.
f(n) = -4*f(n-1)
f(3) = -4*f(3-1)
f(3) = -4*f(2)
f(3) = -4*(-40)
f(3) = 160
In other words "term3 = -4*term2".
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Now do n = 4.
f(n) = -4*f(n-1)
f(4) = -4*f(4-1)
f(4) = -4*f(3)
f(4) = -4*160
f(4) = -640
In other words "4th term = -4*(3rd term)".
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Finally n = 5
f(n) = -4*f(n-1)
f(5) = -4*f(5-1)
f(5) = -4*f(4)
f(5) = -4*(-640)
f(5) = 2560 is the final answer
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What's a shortcut we could use? Notice how we multiply by -4 each time, which indicates the sequence is geometric. The nth term formula would be
f(n) = 10*(-4)^(n-1)
Input n = 5 to get:
f(5) = 10*(-4)^(5-1) = 2560
