Question #42bde

1 Answer
Jim G.
Dec 5, 2017

#a=240" and "r=1/3#

Explanation:

#"the nth term of a geometric progression is"#

#•color(white)(x)a_n=ar^(n-1)#

#rArra_6=ar^5=80/81to(1)#

#rArra_9=ar^8=80/2187to(2)#

#"divide equation "(2)" by equation "(1)#

#rArr(cancel(a) r^8)/(cancel(a) r^5)=(80/2187)/(80/81)#

#rArrr^3=cancel(80)/2187xx81/cancel(80)=1/27#

#rArrr=root(3)(1/27)=1/3#

#"substitute "r=1/3" in equation "(1)#

#rArra(1/3)^5=80/81#

#rArra=(80/81)/(1/243)=(80)/(cancel(81)^1)xxcancel(243)^3/1=240#

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