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?

Question

1404 views around the world

You can reuse this answer
Creative Commons License

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#