1) a₁ = - 17 ; d = 5
an = a₁ + d(n - 1)
a₁₇ = - 17 + 5*(17 - 1) = - 17 + 5*16 = 63
2) 37,33,39..........
a₁1 = 37 ; d = 33 - 37 = - 4
Sn = [2a₁ + d(n - 1)]*n / 2
S₂₀ = [(2*37 - 4*19)*20] / 2 = (74 - 76)*10 = - 20
3) an = 3n - 4;
Sn = [(a₁ + an)*n] / 2
a₁ = 3*1 - 4 = - 1
a₄₀ = 3*40 - 4 = 116
S₄₀ = [(- 1 + 116)*40] / 2 = 115*20 = 2300
4) b₁ = - 81
q = - 1/3
bn = b₁ * q^(n - 1)
b₆ = - 81 * (- 1/3)⁵ = 1/3
5) b₁ = 3
q = 2
Sn = [b₁(1 - q^n)] / (1 - q)
S₄ = [3(1 - 2⁴)] / (1 - 2) = [3*(-15)] / (-1) = 45