The average of a sequence of twenty-five consecutive integers is 'm'

Question

The average of a sequence of twenty-five consecutive integers is 'm', what is the average of the next fifteen consecutive integers?

A. m + 8
B. m + 10
C. m + 15
D. m + 18
E. m + 20

Source : TIME Institute

globaldesi · Accepted Answer

let the firs t term be a
so 25th term = a+24
26th term = a+25
40th term = a+39

now avg of first 25 = first+last/2
or 
 \frac{a+a+24}{2}= m  => m = a+12

now next fifteen terms average
 \frac{a+a+25+39}{2} = a+32 
from first equation a = m-12
or avg = m-12+32
m+20
E

Neha2404 · Answer

Imo-E

Average of 25 consecutive no of =m which is equal to 13th term
Ask- average of next 15 term
1st term in 15 consecutive no= M+12+1=m+13
Last term is =m+12+15=m+27
Average=M+27+m+13/2
 =m+20

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farazmurtaza · Answer

Suppose 1-25 average is 13.. again for next 15 would be 25-40 and it's average is 33. 
Since 
33=13 +20 (m+20)

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Anshul005 · Answer

The average of 25 consecutive numbers is m.

So 13th term is 'm'.

26th term = m + 13 ( 1st term of 15 consecutive terms)

40th term = m + 27 ( 15th term of 15 consecutive terms)

Average of consecutive terms = ( First term + Last term ) / 2

= ( m + 13 + m + 27 ) / 2
 
 = ( 2m + 40 ) / 2

= (m +20)

daniformic · Answer

For me it's easier this way:
1 to 25 (25 terms)
26 to 40 (15 terms)

1: (1+25)/2*(25-1+1)=325/25=13
2: (26+40)/2*(40-26+1)=495/15=33

33-13= 20

Answer->E

MathRevolution · Answer

Let the first number be 'p'

Next numbers will be p + 1, p + 2......

Total consecutive numbers: 25

Average of first 25 numbers :  \frac{(first term + last term) }{ 2}

=> m =  \frac{(p + p + 24) }{ 2}

=> m = p + 12

Next 15 term's average: from  (26)^{th}  to  (40)^{th}  term will be  (32)^{nd}  term

=>  \frac{(p + 25 + p + 39) }{ 2}

=>  \frac{(2p + 64) }{ 2}

=> p + 32

As m = p + 12, therefore,

=> p + 32 = p + 12 + 20 = m + 20

Answer E

Kaifbinarshad · Answer

I have a query here,
What if I take the first sequence from -7,....0,.....+7,then m=0 and the next sequence would be 8,....22,and the average of this sequence is 15,so the average of next fifteen consecutive integer would be m+5..??

Bunuel · Answer

The question is about twenty-five consecutive integers, not fifteen.

The average of a sequence of twenty-five consecutive integers is 'm'

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The average of a sequence of twenty-five consecutive integers is 'm'

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