Sum of 5 consecutive integers
x + ( x +1 ) + ( x +2 ) + ( x + 3 ) + ( x +4 ) = 5n
⇒ 5x + 10 = 5n
⇒ x = ( n – 2 ) ......(i)
Average of 7 consecutive integers
= [( 5x + 10 ) + ( x + 5 ) + ( x + 6 )] / 7
= 7x + 21 / 7
= x + 3 .....(ii)
from eq. (i) and (ii)
New average = x + 3 = ( n – 2 + 3 ) = n + 1
So , the new average increases by 1 .
