Find the sum of the following gp:6,12,24, ... to 10term and 1,-1/2,1/4,1/8,1/16 ... to 20term

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