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The sequence an = 27 ( one third ) ^ n-1 is graphed below. Find the average rate of change between n=2 and n=4

Answer :

apologiabiology
rate of change
find a2 and a4

a2=27(1/3)^(2-1)=27 times 1/3=9
a4=27(1/3)^(4-1)=27 times 1/27=1

rate of change=(a4-a2)/(4-2)=(1-9)/(4-2)=-8/2=-4
average rate of change is -4

The average rate of change between n = 2 and n = 4 is -4.

What is average?

Average is "the number you get when you add two or more figures together and then divide the total by the number of figures you added".

What is average rate?

Average "rate of change between two input values is the total change of function output values divided by change in output value".

According to the question,

aₙ = 27 ([tex]\frac{1}{3}[/tex])⁽ⁿ⁻¹⁾ .

Substitute n = 2 and n = 4 in given equation,

a₂ = 27([tex]\frac{1}{3}[/tex])² ⁻ ¹

a₂ = 9.

a₄ = 27 ([tex]\frac{1}{3}[/tex])⁴⁻¹

a₄ = 27([tex]\frac{1}{3}[/tex])³

a₄ = 1.

Formula to find average rate of change (a₄ - a₂)/(4-2).

=(1-9)/4 = -4.

Hence, the average rate of change between n=2 and n=4 is -4.

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