(i) (a_1=4), (n=25), (a_n=100)

[ S_n = \dfrac{n}{2}(a_1+a_n) = \dfrac{25}{2}(4+100) = \dfrac{25}{2}\cdot104 = 1300 ]

Answer: (1300)

(ii) (a_1=40), (n=20), (d=-3)

[ S_n = \dfrac{n}{2}\bigl[2a_1+(n-1)d\bigr] = \dfrac{20}{2}\bigl[80+19\cdot(-3)\bigr] = 10(80-57)=230 ]

Answer: (230)

(iii) (a_n=52), (n=21), (d=-4)

[ a_n = a_1+(n-1)d \implies 52 = a_1 + 20(-4) \implies a_1 = 52+80=132 ]

[ S_n = \dfrac{21}{2}(132+52) = \dfrac{21}{2}\cdot184 = 1932 ]

Answer: (1932)