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If a sequence of 8 consecutive odd integers with increasing values has

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If a sequence of 8 consecutive odd integers with increasing values has [#permalink]

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If a sequence of 8 consecutive odd integers with increasing values has 9 as its 7th term, what is the sum of the terms of the sequence?

(A) 22
(B) 32
(C) 36
(D) 40
(E) 44
[Reveal] Spoiler: OA

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Re: If a sequence of 8 consecutive odd integers with increasing values has [#permalink]

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New post 09 Nov 2015, 23:26
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Seventh term, a7 = 9
Number of terms,n = 8
an= a1 + (n-1)d
a7= a1 + 6d
=>9 = a1 + 12
=>a1 = -3

8th term , a8 = 11

Sum of terms of the sequence = n/2[first term + last term]
= 4*[-3 + 11]
= 4*8
= 32
Answer B
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Re: If a sequence of 8 consecutive odd integers with increasing values has [#permalink]

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Bunuel wrote:
If a sequence of 8 consecutive odd integers with increasing values has 9 as its 7th term, what is the sum of the terms of the sequence?

(A) 22
(B) 32
(C) 36
(D) 40
(E) 44


Another way to solve is to use the following rule that says, "In a set where the numbers are equally spaced, the mean will equal the median."
For example, in each of the following sets, the mean and median are equal:
{7, 9, 11, 13, 15}
{-1, 4, 9, 14}
{3, 4, 5, 6}

Since we the 8 consecutive odd integers are equally spaced, the median = the mean
The median of the 8 terms will be the average of term4 and term5.

Given: term7 = 9
So, term6 = 7
term5 = 5
term4 = 3

So, the median of the 8 terms = (5 + 3)/2 = 4
So, the MEAN of the 8 terms is also 4

If the mean of the 8 terms = 4, then the SUM of the 8 terms = (8)(4) = 32
Answer: B

Cheers,
Brent
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Re: If a sequence of 8 consecutive odd integers with increasing values has [#permalink]

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New post 10 Nov 2015, 23:11
Bunuel wrote:
If a sequence of 8 consecutive odd integers with increasing values has 9 as its 7th term, what is the sum of the terms of the sequence?

(A) 22
(B) 32
(C) 36
(D) 40
(E) 44



The question has limited number. Using the info of the 7th term=9. So listing the numbers quickly:

11,9,7,5,3,1,-1,-3. The sum=11+9+7+5=32

Answer is B

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Re: If a sequence of 8 consecutive odd integers with increasing values has [#permalink]

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New post 01 Aug 2017, 21:46
Hi Bunuel ,
As per the below question , how we assume that the d=2 ( difference between two odd number is 2 ) . Could you please help .


If a sequence of 8 consecutive odd integers with increasing values has 9 as its 7th term, what is the sum of the terms of the sequence?

(A) 22
(B) 32
(C) 36
(D) 40
(E) 44
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Re: If a sequence of 8 consecutive odd integers with increasing values has   [#permalink] 01 Aug 2017, 21:46
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