Question

describe an infinite geometric series with a beginning value of 2 that converges to 10. what are the first 4 terms of the series

Answer 1

@Shadow

Answer 2

a{1} = first term of series

∞
Infinite Sum =∑ a{1} • r^(n–1) = a{1} ⁄ (1–r)...for any geometric series
n=1


Infinite Sum for this problem = 10 = a{1} ⁄ (1–r)...a{1} = 2 (given)

10 = 2 ⁄ (1–r)

r = 0.8...common ratio

∞
Infinite Sum =∑ 2 • (0.8)^(n–1) ◀◀ (answer)
n=1


a{n}=2 • (0.8)^(n–1)

a{1}=2 • (0.8)^(1–1) = 2

a{2}=2 • (0.8)^(2–1) = 1.6

a{3}=2 • (0.8)^(3–1) = 1.28

a{4}=2 • (0.8)^(4–1) = 1.024

a{5}=2 • (0.8)^(5–1) = 0.8192


Infinite Sum =2 + 1.6 + 1.28 + 1.024 + 0.8192 + . . . + 2•(0.8)^(n–1) ◀◀ (answer)

Answer 3

did u just copy and paste

Answer 4

Mhm (:

Answer 5

Cheese

Answer 6

@Shadow

Answer 7

dw it is right