If the first number of a series is 420 and every number

Question

If the first number of a series is 420 and every number after the first number is multiplied by a fixed constant and the third and fourth terms of this series are 105 and 52.5, respectively, then which of the following represents the sum of the first eight terms of this sequence? 

A) ((420*(1/2^8)+420(1/2^0))/2)*(8)
B) 840*2^7/(1/2^1/3)
C) (8^1/3)*420*((2^7 - 1)/(2^7))/(1/2^8)
D) (7*(8^1/3)*30*(2^8 - 1)/(2^8))/(1/(8^1/3)
E) ((8^1/3)*14*30*(2^8 - 1)/(2^7))/(1/2^1/3)

You got 1.75 min! :snipersmile:

vikramm · Answer

using GM formulae find r first an =ar^n-1 a4=a3*r^2-1 52.5 = 105(r^2-1) => r=1/2 So sum = a1*(1-r^n)/1-r = 420*(1-(1/2)^8)/1-(1/2) = 840(1-(2^-8)) whatever this simplifies to

I think it simplifies to D or E.... I'll pick D

FN · Answer

I dont know about you but A looks straight fwd...

I got A

I assume number 1 thru 8 is not inclusive?

Titleist · Answer

answer is D 

Fresinha - remember that this is a geometric sequence and not a consecutive series. You use the average*number of terms only when finding the sum of a consecutive series. In order to find the sum of a geometric series you use the geometric formula:

a=first term in series
r=constant
n=number of terms

sum of geometric series = a(1-r^n)/(1-r)

=420(1-1/2^8)/(1-1/2) = 420(2^8-1/2^8)/(1/2) = or the answer choice which equals 840(2^8-1)/(2^8)

If the first number of a series is 420 and every number

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards