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What is the value of 10 + 10^3 + 10^6 + 10^9 ?

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Bunuel
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What is the value of 10 + 10^3 + 10^6 + 10^9 ? [#permalink] New post   28 Jul 2021, 02:15
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What is the value of \(10 + 10^3 + 10^6 + 10^9\) ?

A 1,010,101,010
B 1,001,000,010
C 1,001,000,110
D 1,001,001,010
E 100,010,001,010
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D
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errorlogger
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What is the value of 10 + 10^3 + 10^6 + 10^9 ? [#permalink] New post   28 Jul 2021, 02:40
Bunuel wrote:
What is the value of \(10 + 10^3 + 10^6 + 10^9\) ?

A 1,010,101,010
B 1,001,000,010
C 1,001,000,110
D 1,001,001,010
E 100,010,001,010


One can simply add and find (D) as the solution.
However, I was wondering why can't we solve this using GP
a(r^n - 1)/r - 1
10 + 10^3(10^3-1)9 = 111010 - What am I doing wrong here?
chetan2u, Bunuel: Please help here!
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chetan2u
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Re: What is the value of 10 + 10^3 + 10^6 + 10^9 ? [#permalink] New post   28 Jul 2021, 04:02
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errorlogger wrote:
Bunuel wrote:
What is the value of \(10 + 10^3 + 10^6 + 10^9\) ?

A 1,010,101,010
B 1,001,000,010
C 1,001,000,110
D 1,001,001,010
E 100,010,001,010


One can simply add and find (D) as the solution.
However, I was wondering why can't we solve this using GP
a(r^n - 1)/r - 1
10 + 10^3(10^3-1)9 = 111010 - What am I doing wrong here?
chetan2u, Bunuel: Please help here!


the terms are not in GP..
\(10^1, 10^3, 10^6, 10^9\).........only last three terms are in GP
sum=\(10+\frac{a(r^n - 1)}{r - 1}\).........\(a=10^3, n=3, r=10^3\)

\(10+\frac{10^3((10^3)^3-1)}{10^3-1}=10+\frac{1000*999999999}{999}=10+1000*1001001=1001001000+10=10010010010\)
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Re: What is the value of 10 + 10^3 + 10^6 + 10^9 ? [#permalink] New post   28 Jul 2021, 04:08
chetan2u wrote:
errorlogger wrote:
Bunuel wrote:
What is the value of \(10 + 10^3 + 10^6 + 10^9\) ?

A 1,010,101,010
B 1,001,000,010
C 1,001,000,110
D 1,001,001,010
E 100,010,001,010


One can simply add and find (D) as the solution.
However, I was wondering why can't we solve this using GP
a(r^n - 1)/r - 1
10 + 10^3(10^3-1)9 = 111010 - What am I doing wrong here?
chetan2u, Bunuel: Please help here!


the terms are not in GP..
\(10^1, 10^3, 10^6, 10^9\).........only last three terms are in GP
sum=\(10+\frac{a(r^n - 1)}{r - 1}\).........\(a=10^3, n=3, r=10^3\)

\(10+\frac{10^3((10^3)^3-1)}{10^3-1}=10+\frac{1000*999999999}{999}=10+1000*1001001=1001001000+10=10010010010\)


Hi chetan2u, first of all thank you.
If you see my solution above, I also considered only the last 3 terms to be in GP. However, my mistake was that I missed to cube the ratio(r^n). I should have a coffee break for committing such a silly mistake :D
Thanks again :)
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Re: What is the value of 10 + 10^3 + 10^6 + 10^9 ? [#permalink] New post   28 Jul 2021, 05:50
Position of 1 from right in 10 digit number will be 2nd, 4th, 7th and 10th
(D) is the right answer

Bunuel wrote:
What is the value of \(10 + 10^3 + 10^6 + 10^9\) ?

A 1,010,101,010
B 1,001,000,010
C 1,001,000,110
D 1,001,001,010
E 100,010,001,010
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Re: What is the value of 10 + 10^3 + 10^6 + 10^9 ? [#permalink]
28 Jul 2021, 05:50
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