Question

If the sum to n terms of an A.P is cn(n –1); c ≠ 0, then the sum of squares of these terms is

(a) c² n² (n + 1)² 

(b)  2c²/3 n(n - 1)(n - 1)

(c)  2c²/3n(n + 1)(2n + 1)

(d)  None of thes

Answer 1

Correct option (b)  2c²/3  n(n - 1)(n - 1)

Explanation:

T_n = S_n –S_n–1 = cn(n–1) –c(n–1)(n–2)

= c(n–1){n–n+2}

= 2c(n–1)

T_n = 4c² (n–1)²

∴ S_n² = 4c²{0² + 1² + 2² +..................+ (n – 1)²}

=  4c² n(n- 1)(2n - 1)/6

=  2c²/3  n(n - 1)(n - 1)