**Correct option (b) 2c**^{2}/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} = 4c^{2} (n–1)^{2}

∴ S_{n}^{2} = 4c^{2}{0^{2 }+ 1^{2 }+ 2^{2 }+..................+ (n – 1)^{2}}

= 4c^{2} n(n- 1)(2n - 1)/6

= 2c^{2}/3 n(n - 1)(n - 1)