Shayann
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The first five terms of a sequence are shown.

4, 12, 36, 108, 324,

Write an explicit function to model the value of the nth term in the sequence such that f(1) = 4

f(n) =

Please explain!

(I'm doing a practice test, and I'm not sure how to do this, I need an example to help me for when I take the real test. Thank you!)

Respuesta :

it is geometric sequence
because ratio 12/4=3, 36/12= 3 and so on
explicit formula for geometric sequence is f(n)=a(1)*r^(n-1)
explicit means you can find any term of a sequence using 1st term and number n that shows location of the term (second ,third ...and so on)

f(n)=4*3^(n-1)

The explicit function that model the value of the nth term in the sequence such that f(1) = 4 is f(n)= 4 × 3ⁿ⁻¹

4, 12, 36, 108, 324

The sequence follows a geometric pattern. Therefore,

r = 12 / 4 = 3

r = 36 / 12 = 3

r = 108 / 36 = 3

common ratio = r = 3

first term = a = 4

Therefore,

  • f(n)= arⁿ⁻¹

f(n)= 4 × 3ⁿ⁻¹

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