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Math Expert V
Joined: 02 Sep 2009
Posts: 55623
If the terms of a certain sequence are defined by the equation An  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 57% (01:30) correct 43% (01:31) wrong based on 84 sessions

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If the terms of a certain sequence are defined by the equation $$A_n = A_{n-1} + n$$ for all n, what is the value of An in terms of $$A_{n+1}$$?

A. $$A_{n+1} − 1$$

B. $$A_{n+1} + n + 1$$

C. $$A_{n+1} − n$$

D. $$A_{n+1} − n − 1$$

E. $$A_{n+1} − n + 1$$

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Math Expert V
Joined: 02 Aug 2009
Posts: 7743
If the terms of a certain sequence are defined by the equation An  [#permalink]

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Bunuel wrote:
If the terms of a certain sequence are defined by the equation $$A_n = A_{n-1} + n$$ for all n, what is the value of An in terms of $$A_{n+1}$$?

A. $$A_{n+1} − 1$$

B. $$A_{n+1} + n + 1$$

C. $$A_{n+1} − n$$

D. $$A_{n+1} − n − 1$$

E. $$A_{n+1} − n + 1$$

$$A_n = A_{n-1} + n$$
replace all n by n+1. Don't leave the addition of n
$$A_{n+1} = A_n + n+1$$...
So $$A_n = A_{n+1} - n -1$$

D
_________________ V
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Re: If the terms of a certain sequence are defined by the equation An  [#permalink]

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Bunuel wrote:
If the terms of a certain sequence are defined by the equation $$A_n = A_{n-1} + n$$ for all n, what is the value of An in terms of $$A_{n+1}$$?

A. $$A_{n+1} − 1$$

B. $$A_{n+1} + n + 1$$

C. $$A_{n+1} − n$$

D. $$A_{n+1} − n − 1$$

E. $$A_{n+1} − n + 1$$

$$A_{n+1}=A_{n}+n+1$$
$$A_{n}=A_{n+1}-n-1$$
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Senior Manager  S
Joined: 12 Sep 2017
Posts: 263
Re: If the terms of a certain sequence are defined by the equation An  [#permalink]

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chetan2u wrote:
Bunuel wrote:
If the terms of a certain sequence are defined by the equation $$A_n = A_{n-1} + n$$ for all n, what is the value of An in terms of $$A_{n+1}$$?

A. $$A_{n+1} − 1$$

B. $$A_{n+1} + n + 1$$

C. $$A_{n+1} − n$$

D. $$A_{n+1} − n − 1$$

E. $$A_{n+1} − n + 1$$

$$A_n = A_{n-1} + n$$
replace all n by n+1. Don't leave the addition of n
$$A_{n+1} = A_n + n+1$$...
So $$A_n = A_{n+1} - n -1$$

D

Hello chetan2u

Why are you replacing all the n's for n + 1?

Kind regards!
Senior Manager  S
Joined: 12 Sep 2017
Posts: 263
Re: If the terms of a certain sequence are defined by the equation An  [#permalink]

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Bunuel wrote:
If the terms of a certain sequence are defined by the equation $$A_n = A_{n-1} + n$$ for all n, what is the value of An in terms of $$A_{n+1}$$?

A. $$A_{n+1} − 1$$

B. $$A_{n+1} + n + 1$$

C. $$A_{n+1} − n$$

D. $$A_{n+1} − n − 1$$

E. $$A_{n+1} − n + 1$$

Hello Bunuel !

Could you please give an explanation regarding this question?

I don't understand how to disappear the An-1.

Kind regards!
Manager  B
Joined: 15 Nov 2017
Posts: 54
Re: If the terms of a certain sequence are defined by the equation An  [#permalink]

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Hi Bunuel,

Could you please explain in more detail how to solve this problem step-by-step?

Thank you so much!

Bunuel wrote:
If the terms of a certain sequence are defined by the equation $$A_n = A_{n-1} + n$$ for all n, what is the value of An in terms of $$A_{n+1}$$?

A. $$A_{n+1} − 1$$

B. $$A_{n+1} + n + 1$$

C. $$A_{n+1} − n$$

D. $$A_{n+1} − n − 1$$

E. $$A_{n+1} − n + 1$$
Senior Manager  S
Joined: 12 Sep 2017
Posts: 263
If the terms of a certain sequence are defined by the equation An  [#permalink]

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1
Hi KHow !

After some time I underdstood it very well by the following:

An = An-1 + n

Let A1 = 1

So given the formula lets calculate the first values:

A1 = 1
A2 = 1+ 2 = 3
A3 = 3 + 3 = 6
A4 = 6 + 4 = 10

So this means that if we want to calculate An+1 it must be An = An+1 - (n+1) = An = An+1 - n - 1.

Ex.

A3 = An+1 - n - 1

A3 = (An+1 = 10) - ((n-1)) = A4 - 1) = (10 - (4+1)) = 6.
Intern  B
Joined: 12 Feb 2019
Posts: 2
Re: If the terms of a certain sequence are defined by the equation An  [#permalink]

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Hey, not sure why it can't be solved this way:

A(n)=A(n-1) + n
A(n-1)= A(n) - n

A(n+1) + A(n-1) = 2A(n)
A(n+1) + A(n) - n = 2A(n)
A(n+1) - n = A(n)

I will be grateful for explanation what I am calculating wrong Manager  Joined: 20 Dec 2013
Posts: 119
Re: If the terms of a certain sequence are defined by the equation An  [#permalink]

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Bunuel wrote:
If the terms of a certain sequence are defined by the equation $$A_n = A_{n-1} + n$$ for all n, what is the value of An in terms of $$A_{n+1}$$?

A. $$A_{n+1} − 1$$

B. $$A_{n+1} + n + 1$$

C. $$A_{n+1} − n$$

D. $$A_{n+1} − n − 1$$

E. $$A_{n+1} − n + 1$$

We can plug in here.

Let n = 3 and A0 = 4

A0 = 4, A1 = 7 A2 = 10 A3 = 13 A4 = 17
So you are looking for A3 = 13 which is 17 - 3 - 1
Hence D
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