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If 1 + 4 + 7 + ⋯ + x = 70; Then x = ?

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If 1 + 4 + 7 + ⋯ + x = 70; Then x = ?  [#permalink]

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New post 13 Aug 2018, 10:47
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

57% (02:29) correct 43% (02:39) wrong based on 21 sessions

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If \(1+4+7+⋯+x=70\) ; Then \(x=?\)

A) \(11\)
B) \(18\)
C) \(19\)
D) \(20\)
E) \(22\)
Director
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Posts: 504
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Re: If 1 + 4 + 7 + ⋯ + x = 70; Then x = ?  [#permalink]

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New post 13 Aug 2018, 11:00
u1983 wrote:
If \(1+4+7+⋯+x=70\) ; Then \(x\) = \(?\)

A) \(11\)
B) \(18\)
C) \(19\)
D) \(20\)
E) \(22\)


\(x = 3n-2\). Implies, n = 7/8 or x = 19/22.. Substitute this in below equation -
\(70 = n(x+1)/2\)

\(x = 19\)
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Re: If 1 + 4 + 7 + ⋯ + x = 70; Then x = ?  [#permalink]

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New post 13 Aug 2018, 18:49
1
u1983 wrote:
If \(1+4+7+⋯+x=70\) ; Then \(x=?\)

A) \(11\)
B) \(18\)
C) \(19\)
D) \(20\)
E) \(22\)


The given summation series is an Arithmetic Progression(AP) with first term=1, last term=x and common difference=3
nth term of an AP=first term+(n-1)*common difference=1+(n-1)*3=3n-2, So, last term=x=3n-2
We know, sum of 'n' terms =\(\frac{n}{2}\)(first term + last term)
Or, 70=\(\frac{n}{2}\)(1+ 3n-2)
Or, n(3n-1)=140
Or, 3n^2-n-140=0
Or, n=7, \(-\frac{20}{3}\)

So, x=3n-2=3*7-2=19

Ans. (C)
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Re: If 1 + 4 + 7 + ⋯ + x = 70; Then x = ? &nbs [#permalink] 13 Aug 2018, 18:49
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If 1 + 4 + 7 + ⋯ + x = 70; Then x = ?

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