Question

How many terms of the AP 17,15,13,11.... must be added to get the sum 72?Explain the double answer??

Answer 1

Hope it will help you. . . . . . . . .

Answer 2

Answer:

Here ,

a=17 and d=(15-17)=-2

Let the sum of n terms be 72 .Then ,

Sn=72

n/2{2a(n-1)d}

=72

Or n{2×17+(n-1) ×(-2)}=1444

Or n(36-2n)=144 or 2n^2 -36 +144 =0

Or n ^2-18n+72=0 or n^2-12n -6n+72=0

n(n-12)-6(n-12)=0

Or(n-12)(n-6)=0

n=6 or n=12

Hence of first 6 terms =sum of first 12 terms =12

This means that the sum of all terms from 7th to 12th is 0.