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

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Math Expert
Joined: 02 Sep 2009
Posts: 55640
If a sequence of 8 consecutive odd integers with increasing values has  [#permalink]

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09 Nov 2015, 23:12
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Difficulty:

15% (low)

Question Stats:

79% (01:30) correct 21% (01:51) wrong based on 395 sessions

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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

Project PS Butler : Question #101

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Posts: 3782
Re: If a sequence of 8 consecutive odd integers with increasing values has  [#permalink]

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10 Nov 2015, 13:07
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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

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

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10 Nov 2015, 00:26
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1
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
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Re: If a sequence of 8 consecutive odd integers with increasing values has  [#permalink]

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11 Nov 2015, 00:11
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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

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

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

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29 Dec 2018, 03:04
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

Project PS Butler : Question #101

since the 7th term is 9

So the 8 consecutive even numbers are -3,-1,1,3,5,7,9,11

Hence the sum = no.of terms *(first term + last term)/2 = 8 * (-3+11)/2 = 32 hence B)
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Joined: 07 Dec 2014
Posts: 1197
If a sequence of 8 consecutive odd integers with increasing values has  [#permalink]

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29 Dec 2018, 11:09
1
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

mean will be 5th term-1
9-2*2-1=4=mean
8*4=32=sum
B
If a sequence of 8 consecutive odd integers with increasing values has   [#permalink] 29 Dec 2018, 11:09
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