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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: 55668
If a sequence of consecutive integers of increasing value has a sum of  [#permalink]

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12 Dec 2018, 01:29
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25% (medium)

Question Stats:

76% (01:50) correct 24% (02:17) wrong based on 100 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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Re: If a sequence of consecutive integers of increasing value has a sum of  [#permalink]

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12 Dec 2018, 01:38
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, 01:39
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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Re: If a sequence of consecutive integers of increasing value has a sum of  [#permalink]

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07 Jan 2019, 06:40
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
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Joined: 07 Dec 2014
Posts: 1197
If a sequence of consecutive integers of increasing value has a sum of  [#permalink]

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07 Jan 2019, 12:36
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, 02:29
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?
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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, 02:45
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
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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, 02:48
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
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Re: If a sequence of consecutive integers of increasing value has a sum of  [#permalink]

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17 Jan 2019, 10:44
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
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Re: If a sequence of consecutive integers of increasing value has a sum of  [#permalink]

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17 Jan 2019, 10:49
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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Re: If a sequence of consecutive integers of increasing value has a sum of  [#permalink]

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17 Jan 2019, 10:59
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   [#permalink] 17 Jan 2019, 10:59
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