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

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Bunuel
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If a sequence of 8 consecutive odd integers with increasing values has [#permalink] New post   09 Nov 2015, 23:12
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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
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B
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BrentGMATPrepNow
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Re: If a sequence of 8 consecutive odd integers with increasing values has [#permalink] New post   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
Answer: B

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

Answer is B
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Re: If a sequence of 8 consecutive odd integers with increasing values has [#permalink] New post   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


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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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Re: If a sequence of 8 consecutive odd integers with increasing values has [#permalink] New post   Updated on: 11 Apr 2020, 11:44
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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


mean will be 5th term minus 1,
or 9-(2*2)-1=4
so 8*4=32 sum
B

Originally posted by gracie on 29 Dec 2018, 11:09.
Last edited by gracie on 11 Apr 2020, 11:44, edited 1 time in total.
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Re: If a sequence of 8 consecutive odd integers with increasing values has [#permalink] New post   10 Apr 2020, 10:09
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7th term=9
8th term=11
Sm={2a+(n-1)d}n/2
Let the "a" i.e first term be 11 ( 8th term) and d=-2 Converted the A.P in a decreasing order A.P
Putting the values of n,a & d in eq===>(22-14)4
===> 32 ANS
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Re: If a sequence of 8 consecutive odd integers with increasing values has [#permalink] New post   10 Apr 2020, 11:53
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


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if 7th term=9,
then 1st term=9-6*2=-3,
8th term=9+1*2=11,
and sum of sequence=8(-3+11)/2=32
B
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Re: If a sequence of 8 consecutive odd integers with increasing values has [#permalink] New post   29 Apr 2020, 09:16
In a list of 8 consecutive odd integers if 7th term is "9" the next and the last term will be "11".

we can solve it using a sum of an A.P. (Arithmetic progression) formula, by considering the last term as the first term (11) and difference (-2).

The formula goes as: S = n/2(2a + (n-1)d)
Where n is the number of terms= 8
a is the first term = 11
and d the common difference = -2

8/2(2*11 + (8-1)(-2))

=4(22-14)
=4*8
= 32

Option B
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Re: If a sequence of 8 consecutive odd integers with increasing values has [#permalink] New post   19 Mar 2024, 07:32
 
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

­
Attachment:
Screenshot 2024-03-19 200104.png
Screenshot 2024-03-19 200104.png [ 1.45 KiB | Viewed 535 times ]
Add the numbers, Answer will be (B) 32
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Re: If a sequence of 8 consecutive odd integers with increasing values has [#permalink]
19 Mar 2024, 07:32
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