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

Question

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

BrentGMATPrepNow · Accepted Answer

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

Skywalker18 · Answer

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 
 = 4* 
 = 4*8 
 = 32
Answer B

Mo2men · Answer

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

shuvodip04 · Answer

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)

gracie · Answer

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

varun325 · Answer

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

gracie · Answer

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

Shrey08 · Answer

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

Abhishek009 · Answer

Screenshot 2024-03-19 200104.png Add the numbers, Answer will be (B) 32

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

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