Answer:
Sₙ = 6 x (1 - 2¹⁰) / (1 - p) = 6 x 1023 = 6138
S'ₙ =2.52
Step-by-step 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
