A series has three numbers, a, ar and ar^2. In the series, the first..

Question

A series has three numbers, a, ar and ar^2. In the series, the first term is twice the second term. What is the ratio of sum of the first two terms to the sum of the last two terms in series?

A. 1:1

B. 1:2

C. 1:4

D. 2:1

E. 4:1

niks18 · Accepted Answer

Given  a=2ar , or  r=\frac{1}{2}

Hence the terms are  a ,  \frac{a}{2}  &  \frac{a}{4}

Ratio  = (a+\frac{a}{2})/(\frac{a}{2}+\frac{a}{4})=\frac{2}{1}

Option  D

doeadoer · Answer

The ans should be 2:1.
Though I read the question incorrect as the first term being half of the second term.

BigUD94 · Answer

Wouldn't ar^2 become a^2/4?

niks18 · Answer

Hi  BigUD94 
Here it is r^2 and not a^2, hence it will be a/4 when you substitute the value of r.

Posted from my mobile device

BigUD94 · Answer

niks18

Oh alright sir I thought it was (ar)^2 by mistake, I got it now. Thanks

niks18 · Answer

Hi BigUD94 you suddenly made me 50 year old guy by writing that "sir"

chetan2u · Answer

Such Questions can be done in two ways..

Algebraic as shown above
 2ar=a......r=\frac{1}{2} ...
So terms are a, a/2 and a/4..
Now (a+a/2)/(a/2+a/4)=(3a/2)/(3a/4)=4/2=2/1...
2:1

Other slightly easier is substitution, rather smart substitution looking at the question
Let a=4..
So ar will be half, 4/2=2
And ar^2 will become 2/2=1
Number 4,2,1...
We are looking for  \frac{4+2}{2+1}=\frac{6}{3}= 
So 2:1

BigUD94 · Answer

niks18

Har koi gyaani hai idhar, mu se sir nikal hi jaata hai out of respect :D

generis · Answer

chetan2u  , I like this second method. I'm a little confused by this part:
 
Why is third term derived from 2/2? I thought it would be:
 a = 4 
 a_2 = 4 * \frac{1}{2} = 2 
 a_3 = 4 * \frac{1}{4} = 1

I'm missing something about what happened to ratio, r, here . . .

chetan2u · Answer

Hi..

No you are correct, both mean the same thing...
you have taken  \frac{4}{4}=4*\frac{1}{4}  as  a*r^2 , that is first term * r^2
whereas in my calculations ...  \frac{2}{2}=2*\frac{1}{2}  as  ar*r , that is 2nd term * r

generis · Answer

chetan2u  , thanks! My brain short-circuited. I appreciate the help.

jfranciscocuencag · Answer

Good night!

Could someone please explain to me how do everyone is arriving to r = 1/2?

Why can't we consider ar as a whole term?

A1 = a = 4
A2 = ar = 2
A3 = ar2 = 4

I mean, do I have to separate different letters in all the sequence questions?

Kind regards!!!

KanishkM · Answer

Given a =2 ar, then r =1/2

Now put back value of r in a, ar , ar^2

a + ar = 3a / 2 --------------------(x)
ar + ar^2 = 3a/4 -----------------(y)

Ratio of (x)/(y)

D

KanishkM · Answer

Hi  jfranciscocuencag

I would like to share my thoughts on this, Its written in the question, that it is a series.

So a ar ar^2, signifies that it is a  Geometric Progression , in which the common ratio(r) is equal

ar/a = ar^2/ar --------(x)

So now if you now that relationship, you can even calculate it like that

Its given a= 2 ar, when you substitute this in (x) you can get LHS as 1/2, which will be equal to RHS.

But you need not write all of this, while solving this question, since you know  this   you can directly solve.

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A series has three numbers, a, ar and ar^2. In the series, the first..

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