Describe an infinite geometric series with a beginning value of 2 that converges to 10. What are the first four terms of the sequence?
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)
2 answers
is this right???
correct all the way. Good work.
1 answer