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?

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Answer 1 · 2018-05-30T11:42:34

#a_n= 130+175(n-1)#

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#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#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#