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# In the infinite sequence a1, a2, ..., an, an equals the sum of all pre

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In the infinite sequence a1, a2, ..., an, an equals the sum of all pre  [#permalink]

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23 Nov 2016, 05:33
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Difficulty:

65% (hard)

Question Stats:

58% (02:48) correct 42% (02:39) wrong based on 98 sessions

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In the infinite sequence $$a_1$$, $$a_2$$, ..., $$a_n$$, $$a_n$$ equals the sum of all previous values in the sequence for all values n>2. If $$a_1=1$$ and $$a_3=3$$, what is the value of $$\frac{a_{100}}{a_{97}}$$?

A. 3
B. 8
C. 12
D. 27
E. 48

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Re: In the infinite sequence a1, a2, ..., an, an equals the sum of all pre  [#permalink]

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24 Nov 2016, 02:01
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Given: $$a_{1} = 1; a_{3} = 3; a_{2} = a_{3} - a_{1} = 2$$

Sequence: 1, 2, 3, 6, 12, 24 ........ --> Notice that for n > 3, each term is double the previous term
i.e. $$a_{6} = 2a_{5} = 4a_{4}$$

Similarly, $$a_{100} = 2a_{99} = 4a_{98} = 8a_{97}$$

$$a_{100}/a_{97} = 8{a_{97}/a_{97}} = 8$$

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Re: In the infinite sequence a1, a2, ..., an, an equals the sum of all pre  [#permalink]

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25 Nov 2016, 16:46
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Using the GP, the CR is 2

General Sum formula for GP =b1*r^n-1/r-1

First term b1 =1; r =2

a100/a97 =2^99/2^96 =2^3 =8 =B
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In the infinite sequence a1, a2, ..., an, an equals the sum of all pre  [#permalink]

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23 Jun 2017, 04:06
Using the GP, the CR is 2

General Sum formula for GP =b1*r^n-1/r-1

First term b1 =1; r =2

a100/a97 =2^99/2^96 =2^3 =8 =B

I see that the GP sum formula is [a * ( 1 - r^n) ] / 1 - r. Can you please elaborate on how you got the mentioned formula?
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Re: In the infinite sequence a1, a2, ..., an, an equals the sum of all pre  [#permalink]

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24 Dec 2017, 02:03
Bang2919 wrote:
Using the GP, the CR is 2

General Sum formula for GP =b1*r^n-1/r-1

First term b1 =1; r =2

a100/a97 =2^99/2^96 =2^3 =8 =B

I see that the GP sum formula is [a * ( 1 - r^n) ] / 1 - r. Can you please elaborate on how you got the mentioned formula?

Hi,

The formula which you're talking about is used when R<1
Here, we have R>1 which is 2 so that formula is used

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Re: In the infinite sequence a1, a2, ..., an, an equals the sum of all pre  [#permalink]

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17 Feb 2019, 08:06
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Re: In the infinite sequence a1, a2, ..., an, an equals the sum of all pre   [#permalink] 17 Feb 2019, 08:06
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# In the infinite sequence a1, a2, ..., an, an equals the sum of all pre

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