Question

Find the average of even numbers from 60 to 245

Answer 1

Consider it as an ap, 60,62.....244(245 is not even so it is not taken)

Here a=60,an=244(the last even no of the ap) d=2

An=a+(n-1)d

244=60+(n-1)2

244=60+2n-2

=58+2n

244-58/2=n,n=93

Now that we know n lets find the avg

Avg=sum of ap/n

=[N/2(2a+(n-1)d]/N

=2a+(n-1)d/2

2(60)+(93-1)2/2

Taking 2 outside

2[60+92]/2

=60+92=152

The avg is 152