find the sum of the following gp:6,12,24,......to 10term and 1,1/2,1/4,1/8,1/16.........to 20term
Mathematics
joanozuah
Question
find the sum of the following gp:6,12,24,......to 10term and 1,1/2,1/4,1/8,1/16.........to 20term
1 Answer

1. User Answers kenlingdad
Answer:
Sₙ = 6 x (1  2¹⁰) / (1  p) = 6 x 1023 = 6138
S'ₙ =2.52
Stepbystep explanation:
sum of this sequence: Sₙ = A₁ x (1  pⁿ) / (1  p)
Sₙ: sum of n terms
A₁: initial value 6
p: common ratio 2
n: terms 10
Sₙ = 6 x (1  2¹⁰) / (1  p) = 6 x 1023 = 6138
Is there any mistake in the 2nd question  about the common ratio (1/2)?
S'ₙ =1 + (1/2) + 1 x (1  (1/2)¹⁸)) / (1  (1/2)) = 1/2 + 2 x (1  (1/2)¹⁸)
S'ₙ = 1/2 + 2 x (1  1/262144) = 1/2 + 262143/130072= 0.5 +2.02 = 2.52