Question

prove that the sum of any number of terms of the a.p 16,24,32,..starting from the first, added to 9 gives a perfect square​

Answer 1

Answer:

Step-by-step explanation:

16,24,32,,................

here a=16,d=8

so

Sn=n/2(2*16+(n-1)8)

=n/2(32 +8n-8)

=n/2(8n+24)

Sn=n(4n+12)=4n²+12n

Adding 9 both sides

Sn+9=4n²+12n+9

=(2n)²+2*2n*3+(3)²

Sn+9=(2n+3)²

hence Sn+9 is a perfect square

hence proved