Question

prove that if,9 is added to the number of first few terms of an arithmetic sequence:16,24,23,.......... gives a perfect square.

Answer 1

Step-by-step explanation:

a=16

d = 24-16 = 8

Let number of terms = n

Sn = n(2×a+(n-1)×d)/2

=n(2×16+(n-1)×8)/2

= n(12 + 4n)

Sn + 9 = 4n2 + 12n + 9 = (2n + 3)2

hence,if 9 is added to the number of first few terms of an arithmetic sequence:16,24,23,.......... gives a perfect square.

hope it helps