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# If a sequence of consecutive integers of increasing value has a sum of

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Math Expert
Joined: 02 Sep 2009
Posts: 52294
If a sequence of consecutive integers of increasing value has a sum of  [#permalink]

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12 Dec 2018, 00:29
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Difficulty:

25% (medium)

Question Stats:

72% (01:02) correct 28% (01:29) wrong based on 72 sessions

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If a sequence of consecutive integers of increasing value has a sum of 63 and a first term of 6, how many integers are in the sequence?

(A) 11
(B) 10
(C) 9
(D) 8
(E) 7

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VP
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Location: India
Concentration: Sustainability, Marketing
WE: Marketing (Energy and Utilities)
Re: If a sequence of consecutive integers of increasing value has a sum of  [#permalink]

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12 Dec 2018, 00:38
1
Bunuel wrote:
If a sequence of consecutive integers of increasing value has a sum of 63 and a first term of 6, how many integers are in the sequence?

(A) 11
(B) 10
(C) 9
(D) 8
(E) 7

sn= n/2 ( 2a+ (n-1)d)

63= n/2 ( 12+n-1)

solve for n we get n = 7

IMO E
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Re: If a sequence of consecutive integers of increasing value has a sum of  [#permalink]

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12 Dec 2018, 00:39
1
$$S_n = \frac{n}{2}[2a+(n-1)d]$$
$$a = 6$$
$$d = 1$$
$$S_n = 63$$
$$63 = \frac{n}{2}[12+n-1]$$
$$126 = n^2+11n$$
$$n^2+11n-126 = 0$$
$$n^2+18-7n-126 = 0$$
n = 7 or -18
n cannot be negative

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If you are not badly hurt, you don't learn. If you don't learn, you don't grow. If you don't grow, you don't live. If you don't live, you don't know your worth. If you don't know your worth, then what's the point?

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Joined: 15 Nov 2017
Posts: 23
Re: If a sequence of consecutive integers of increasing value has a sum of  [#permalink]

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07 Jan 2019, 05:40
Hi Bunuel,

Could you please provide your feedback on how to solve this problem? I am stuck on C; however, the correct answer is E.

Thank you!

Bunuel wrote:
If a sequence of consecutive integers of increasing value has a sum of 63 and a first term of 6, how many integers are in the sequence?

(A) 11
(B) 10
(C) 9
(D) 8
(E) 7
VP
Joined: 07 Dec 2014
Posts: 1152
If a sequence of consecutive integers of increasing value has a sum of  [#permalink]

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07 Jan 2019, 11:36
1
Bunuel wrote:
If a sequence of consecutive integers of increasing value has a sum of 63 and a first term of 6, how many integers are in the sequence?

(A) 11
(B) 10
(C) 9
(D) 8
(E) 7

because 63 sum=number of terms*mean,
try choices 9 and 7 as factors of 63
7 terms with mean of 9 works
E
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Joined: 04 Jan 2018
Posts: 13
Re: If a sequence of consecutive integers of increasing value has a sum of  [#permalink]

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16 Jan 2019, 01:29
Afc0892 wrote:
$$S_n = \frac{n}{2}[2a+(n-1)d]$$
$$a = 6$$
$$d = 1$$
$$S_n = 63$$
$$63 = \frac{n}{2}[12+n-1]$$
$$126 = n^2+11n$$
$$n^2+11n-126 = 0$$
$$n^2+18-7n-126 = 0$$
n = 7 or -18
n cannot be negative

Could you please explain why have you taken D=1?
Director
Joined: 18 Jul 2018
Posts: 573
Location: India
Concentration: Finance, Marketing
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Re: If a sequence of consecutive integers of increasing value has a sum of  [#permalink]

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16 Jan 2019, 01:45
1
Afc0892 wrote:
$$S_n = \frac{n}{2}[2a+(n-1)d]$$
$$a = 6$$
$$d = 1$$
$$S_n = 63$$
$$63 = \frac{n}{2}[12+n-1]$$
$$126 = n^2+11n$$
$$n^2+11n-126 = 0$$
$$n^2+18-7n-126 = 0$$
n = 7 or -18
n cannot be negative

Could you please explain why have you taken D=1?

Consecutive integers have a difference of 1. Hence D = 1.

Posted from my mobile device
_________________

If you are not badly hurt, you don't learn. If you don't learn, you don't grow. If you don't grow, you don't live. If you don't live, you don't know your worth. If you don't know your worth, then what's the point?

Intern
Joined: 04 Jan 2018
Posts: 13
Re: If a sequence of consecutive integers of increasing value has a sum of  [#permalink]

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16 Jan 2019, 01:48
Afc0892 wrote:
Afc0892 wrote:
$$S_n = \frac{n}{2}[2a+(n-1)d]$$
$$a = 6$$
$$d = 1$$
$$S_n = 63$$
$$63 = \frac{n}{2}[12+n-1]$$
$$126 = n^2+11n$$
$$n^2+11n-126 = 0$$
$$n^2+18-7n-126 = 0$$
n = 7 or -18
n cannot be negative

Could you please explain why have you taken D=1?

Consecutive integers have a difference of 1. Hence D = 1.

Posted from my mobile device

Damn, I completely missed the term consecutive. Thank you
Intern
Joined: 16 Jul 2018
Posts: 26
Re: If a sequence of consecutive integers of increasing value has a sum of  [#permalink]

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17 Jan 2019, 09:44
Archit3110 Afc0892

Hey guys I know that the general formula is (Afist+A final)n/2 how did u come up with this one sn= n/2 ( 2a+ (n-1)d) ?
I would really appreciate some help, thank you in advance
VP
Joined: 18 Aug 2017
Posts: 1248
Location: India
Concentration: Sustainability, Marketing
WE: Marketing (Energy and Utilities)
Re: If a sequence of consecutive integers of increasing value has a sum of  [#permalink]

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17 Jan 2019, 09:49
1
UNSTOPPABLE12 wrote:
Archit3110 Afc0892

Hey guys I know that the general formula is (Afist+A final)n/2 how did u come up with this one sn= n/2 ( 2a+ (n-1)d) ?
I would really appreciate some help, thank you in advance

UNSTOPPABLE12
its a general formula to determine sum of no in a sequence .
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Intern
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Posts: 26
Re: If a sequence of consecutive integers of increasing value has a sum of  [#permalink]

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17 Jan 2019, 09:59
KHow

An another easy way to solve this without using formulas would just be to calculate that is the way I did it.

6 is the starting point, and you know that the numbers are consecutive, fortunately the sum is really low (63) thus calculating is feasible within a small time frame.

6+7+8+9+10+11+12=63, thus the answer is 7
Re: If a sequence of consecutive integers of increasing value has a sum of &nbs [#permalink] 17 Jan 2019, 09:59
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