If the sum of the smallest and the largest numbers in a sequence of 7

Question

If the sum of the smallest and the largest numbers in a sequence of 7 consecutive odd integers is 114, what is the average (arithmetic mean) of these seven integers?

A. 19
B. 38
C. 57
D. 76
E. 114

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culpavoluptatum · Answer

If the numbers are 7 consecutive odd integers then the sequence can be like this: 
Assuming 1st number from the sequence be x.
x, x+2, x+4, x+6, x+8, x+10, x+12

Question tells us that the sum of 1st and the 7th number is equal to 114.
i.e., x + (x+12) = 114
2x = 114 - 12
2x = 102
x = 51

Sequence will be; 51, 53, 55, 57, 59, 61, 63
As these terms are equidistant and the number of terms in the sequence is odd. Which means middle term is the mean of the sequence.

Answer C. 57

icandoit4u · Answer

Ans - C - 57 
we are already given the sum of the largest and smaller number in a sequence, so the find the average we can just divide the sum by 2 to get the average ,this is possible if the sequence is in AP, which is 114/2=57 , this is so because the terms equidistant, so the sum of corresponding number at each end of the sequence when divided by 2 will give u the average . for eg 2, 5, 8, 11, 14, 17, 20, so the average here is 11, but if u add the ends 2+20/2 = 11, 5+17/2 = 11 and so on.

TheAdmissionHub · Answer

Let x be the smallest integer of the sequence.
The sequence can be written as:  x, x+2, x+4, x+6, x+8, x+10, x+12

We know that the sum of the smallest and largest integer is  114: x+(x+12)=114  ⭢  x=51

Therefore, the sequence is:  51, 53, 55, 57, 59, 61, 63 .

Since they are all equally distant, the average will be the number in the middle of the sequence, which is  57 .

Answer: C

gautamK0206 · Answer

Let the consecutive odd numbers be represented as  a-6, a-4, a-2, a, a+2, a+4, a+6 .
We are given the sum of the smallest and the largest numbers, a-6 + a+6 = 114, giving, a = 57.
Now, to find the average (arithmetic mean) = (a-6+a-4+a-2+a+a+2+a+4+a+6) / 7
7a/7 = a = 57
Therefore,  the correct answer is C. 57

Shinz · Answer

I found a very easy way for this, 
We know the concept that Average = sum/no of terms
and we know that first(a) and last(l) element of the 7 odd sequence is 114.

by the Arithmetic formulae: sum = n/2(a+l) ------- where n = no of terms, a = first term, l=last term
so, replacing we get : average(n) = n/2(a+l)
average = (a+l)/2
average = 57

If the sum of the smallest and the largest numbers in a sequence of 7

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If the sum of the smallest and the largest numbers in a sequence of 7

Prep Toolkit

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