A G.P series problem

Algebra Level 3

a,b,c,d are in G.P a+9=c d+18=b.

Find a+b+c+d

-12 12 15 -15

1 solution

Sanjeet Raria
Oct 15, 2014

Let the terms of the GP be $a=a, b=ar, c=ar^2, c=ar^3$ . Now $a+9=c$ $\Rightarrow a+9=ar^2$ Multiplying by $r$ we get, $ar+9r=ar^3...(1)$ And $b+18=d$ $\Rightarrow ar+18=ar^3…(2)$ Subtracting (1) from (2) & solving we finally get, $\Large a=3, r=-2$ $a+b+c+d=a(1+r+r^2+r^3)=3(1-2+4-8)=\boxed{-15}$

values can be 3,6,12,24.It satisfies all condition. Its sum is 45

Saurav Sah - 6 years, 7 months ago

It do not satisfy that d+18=b(6+18≠32)

Kalpok Guha - 6 years, 6 months ago

A G.P series problem

1 solution

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