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Integer x equals the number of terms of an arithmetic progression and

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gracie
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Integer x equals the number of terms of an arithmetic progression and [#permalink] New post   02 Mar 2019, 21:51
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Integer x equals the number of terms of an arithmetic progression and it's common difference. If the range of the progression is 6x, what is the value of x?

A. 3
B. 5
C. 7
D. 9
E. 11
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Re: Integer x equals the number of terms of an arithmetic progression and [#permalink] New post   02 Mar 2019, 22:57
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gracie wrote:
Integer x equals the number of terms of an arithmetic progression and it's common difference. If the range of the progression is 6x, what is the value of x?

A. 3
B. 5
C. 7
D. 9
E. 11



Let the common difference be d, and the first element be a.
so \(d=x\), and last term = \(a+(x-1)d\)..

Now RANGE = last term-first term = \((a+(x-1)d)-1=(x-1)d=6x\)
Substitute d=x, so \((x-1)x=6x.....x-1=6\) or \(x=7\)
We cancelled out x from both sides as x cannot be 0.

C
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Re: Integer x equals the number of terms of an arithmetic progression and [#permalink] New post   03 Mar 2019, 00:49
gracie wrote:
Integer x equals the number of terms of an arithmetic progression and it's common difference. If the range of the progression is 6x, what is the value of x?

A. 3
B. 5
C. 7
D. 9
E. 11


Hi,

Given:
n=d=x,
Range = nth term - 1st term = 6x
a+(n-1)d-a = 6x
(x-1)x = 6x
x-1 = 6
x = 7

Option C

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Re: Integer x equals the number of terms of an arithmetic progression and [#permalink] New post   03 Mar 2019, 07:47
chetan2u wrote:
gracie wrote:
Integer x equals the number of terms of an arithmetic progression and it's common difference. If the range of the progression is 6x, what is the value of x?

A. 3
B. 5
C. 7
D. 9
E. 11



Let the common difference be d, and the first element be a.
so \(d=x\), and last term = \(a+(x-1)d\)..

Now RANGE = last term-first term = \((a+(x-1)d)-1=(x-1)d=6x\)
Substitute d=x, so \((x-1)x=6x.....x-1=6\) or \(x=7\)
We cancelled out x from both sides as x cannot be 0.

C





Hello Chetan Sir,

Just a query..

X equals Y and Z means mean X=Y ,X=Z

I initially assumed this wrong int this question .
x= NUMBER OF terms of AP + Common diffrerence..

I guess this was wrong .
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Re: Integer x equals the number of terms of an arithmetic progression and [#permalink] New post   18 May 2020, 09:15
gracie wrote:
Integer x equals the number of terms of an arithmetic progression and it's common difference. If the range of the progression is 6x, what is the value of x?

A. 3
B. 5
C. 7
D. 9
E. 11


Given: Integer x equals the number of terms of an arithmetic progression and it's common difference.

Asked: If the range of the progression is 6x, what is the value of x?

Let a be first term, n be number of terms and d be common difference of the arithmetic progression

n = x; d = x
Range = l - a = a + (n-1)d = (n-1)d = (x-1)x = 6x; x-1 = 6; x =7

IMO C
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Re: Integer x equals the number of terms of an arithmetic progression and [#permalink] New post   21 Jan 2024, 12:55
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Re: Integer x equals the number of terms of an arithmetic progression and [#permalink]
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