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VP  P
Joined: 07 Dec 2014
Posts: 1229
The first term, the mean, the last term, and the sum of an arithmetic  [#permalink]

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8 00:00

Difficulty:   65% (hard)

Question Stats: 63% (02:40) correct 38% (02:41) wrong based on 56 sessions

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The first term, the mean, the last term, and the sum of an arithmetic progression of nine terms are all perfect squares. What is the sum of these four squares?

A. 289
B. 300
C. 376
D. 415
E. 487
##### Most Helpful Community Reply
VP  P
Joined: 07 Dec 2014
Posts: 1229
The first term, the mean, the last term, and the sum of an arithmetic  [#permalink]

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3
2
jfranciscocuencag wrote:
gracie

Hello!

Could you please provide an answer?

Regards!

hi,

let x=first term
y=last term
sum of four squares=x+y+(x+y)/2+[(x+y)/2]9➡
6(x+y)
300 is only multiple of 6
x=1, y=49, mean=25, sum=225
1+49+25+225=300
B

I hope this helps.
##### General Discussion
Senior Manager  S
Joined: 12 Sep 2017
Posts: 297
Re: The first term, the mean, the last term, and the sum of an arithmetic  [#permalink]

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1
gracie

Hello!

Could you please provide an answer?

Regards!
Intern  B
Joined: 18 Oct 2017
Posts: 1
Re: The first term, the mean, the last term, and the sum of an arithmetic  [#permalink]

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Hi Grace,

Can you please explain why did you multiply 9 with the mean?

Regards,
JM
VP  P
Joined: 07 Dec 2014
Posts: 1229
Re: The first term, the mean, the last term, and the sum of an arithmetic  [#permalink]

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JimitMehta wrote:
Hi Grace,

Can you please explain why did you multiply 9 with the mean?

Regards,
JM

hi, JM

because there are 9 terms in the sequence.
9 terms*mean (25)=sum of total sequence (225)

I hope this helps,
gracie
Intern  B
Joined: 12 Feb 2018
Posts: 13
Re: The first term, the mean, the last term, and the sum of an arithmetic  [#permalink]

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3
Let the sequence be a-4d, a-3d, a-2d, a-d, a, a+d, a+2d, a+3d, a+4d

First term + Last term + mean + sum of terms = a-4d + a+4d + a + 9a = 12a

The only term divisible by 12 is 300
Intern  B
Joined: 20 Nov 2017
Posts: 3
Re: The first term, the mean, the last term, and the sum of an arithmetic  [#permalink]

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I solved it this way.

take the first number as 6, 2nd number as 10, then the mean becomes 8 [ Essentially the 3-4-5 triangle rule as only that can be an equally spaced set of squares ]
the addition of the squares of all three gives 200. subtracting it from the answer choices given, Only 300 yields a perfect square i.e. 100
Ans. B
Senior Manager  S
Joined: 12 Sep 2017
Posts: 297
The first term, the mean, the last term, and the sum of an arithmetic  [#permalink]

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1
gracie wrote:
jfranciscocuencag wrote:
gracie

Hello!

Could you please provide an answer?

Regards!

hi,

let x=first term
y=last term
sum of four squares=x+y+(x+y)/2+[(x+y)/2]9➡
6(x+y)
300 is only multiple of 6
x=1, y=49, mean=25, sum=225
1+49+25+225=300
B

I hope this helps.

Hello gracie!

Could you please help me with the following?

How could it be 49 the last term if its an arithmetic progression of 9 terms?

Shouldn't be:

nth = a + d(n-1)

1(a),4,9,16,25(mean),36,49,64,81... 9 terms in total.

So

a = 1
nth = 81
Mean = 25
Sum of terms = 285

Mmmm now that I am writing it I guess is wrong cuz it should be a geometric progression, isn't it?
Manager  B
Joined: 09 Jun 2017
Posts: 106
GMAT 1: 640 Q44 V35 Re: The first term, the mean, the last term, and the sum of an arithmetic  [#permalink]

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guys , let the arithmetic progression of nine terms be x
so what is the sum of an arithmetic progression of nine terms ? 8x or 9x ?
_________________
Hope this helps
Give kudos if it does Re: The first term, the mean, the last term, and the sum of an arithmetic   [#permalink] 14 Apr 2019, 03:15
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# The first term, the mean, the last term, and the sum of an arithmetic

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