A new golf course has 480 lifetime members 3 weeks after it opens and 1005 lifetime members 6 weeks after it opens. Assume the membership increase is arimethic, what is the general term that represents the sequence for this situation?

1 Answer
May 30, 2018

a_n= 130+175(n-1)

Explanation:

Let the ith term be a_i

Let the difference between sequential terms be d

Then we have:

i=1->a_1=a_1+0d
i=2->a_2=a_1+1d
i=3->a_3=a_1+2d=480
i=4->a_4=a_1+3d
i=5->a_5=a_1+4d
i=6->a_6=a_1+5d=1005

i=n->a_n=a_1+(n-1)d
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color(brown)("Now to determine the value of "d)

a_1+2d=480" "..........................Equation(1)
a_1+5d=1005" "........................Equation(2)

Equation(2)-Equation(1) gives:

3d=525

Divide both sides by 3

color(blue)(d=175)

color(brown)("Now determine the value of "a_1)

So by substitution inro Eqn(1)we have:

a_1+2(175)=480

a_1=130

General formula ->a_n= 130+175(n-1)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(brown)("Check")

a_3=130+2(175)=480

a_6=130+5(175)= 1005