Question

There are 7 consecutive integers. The average of first 5 is A. The average of all 7 integers will be?

Answer 1

Let the first term be x, and the succeding terms x+1,x+2,.....x+6

Now,

[x+(x+1)+(x+2)+(x+3)+(x+4)]/5=A

(5x+10)/5=A

x+2=A

x=A-2 ⇒(i)

So,

Average of all 7 integers,

=[5x+10 +(x+5)+(x+6)]/7

=(7x+21)/7

=x+3

=A-2+3

=A+1   [from (i)]

Answer 2

Answer:

   I hope it will help u

1, 2, 3, 4, 5, 6, 7

Here number of values are 7, and difference between two consecutive values is equal, therefore average of this series is middle number = (1+ total terms)th/2 = 4th term = 4

Proof: average = sum of numbers/ total number of values

= (1+2+3+4+5+6+7)/7 = 28/7 = 4

In similar way we have average of first 7 integers of an odd number series is 37

Average of 7 terms is 4th term = 37

and average of 13 terms = (1+13)/2 = 7th term

4th term = 37

5th = 39

6th = 41

7th = 43 (Ans)

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