If S19 = 570 and A1= -6 in an arithmic sequence find d, and A30

Question

If S19 = 570 and A1= -6 in an arithmic sequence find d, and A30

Answer 1

S₁₉=570 = n(a₁ + a₁₉)/2

 

times 2

 

1140 = 19(-6 + a₁₉)

 

divide by 19

 

60 = -6 + a₁₉

 

a₁₉ = 66

 

d = (66--6)/18

 

d = 4

 

so the common difference = 4

 

a₃₀ = -6 + 4(29)

 

= -6 +116

 

a₃₀ = 110