A sequence can be generated by using gn = 2(gn-1), where g1= 1/3 and n is a whole number greater than 1. What are the first 5 terms of the sequence?
To generate the sequence, we can apply the given formula repeatedly.
First term (n=1):
g1 = 1/3
Second term (n=2):
g2 = 2(g2-1) = 2(g1) = 2(1/3) = 2/3
Third term (n=3):
g3 = 2(g3-1) = 2(g2) = 2(2/3) = 4/3
Fourth term (n=4):
g4 = 2(g4-1) = 2(g3) = 2(4/3) = 8/3
Fifth term (n=5):
g5 = 2(g5-1) = 2(g4) = 2(8/3) = 16/3
Therefore, the first five terms of the sequence are 1/3, 2/3, 4/3, 8/3, and 16/3.
To find the first 5 terms of the sequence, we can use the given formula.
Given: g₁ = 1/3 and the formula gn = 2(gn-1)
Let's calculate the first 5 terms step-by-step:
Term 1 (n=1):
g₁ = 1/3
Term 2 (n=2):
g₂ = 2(g₂-1) = 2(g₁) = 2(1/3) = 2/3
Term 3 (n=3):
g₃ = 2(g₃-1) = 2(g₂) = 2(2/3) = 4/3
Term 4 (n=4):
g₄ = 2(g₄-1) = 2(g₃) = 2(4/3) = 8/3
Term 5 (n=5):
g₅ = 2(g₅-1) = 2(g₄) = 2(8/3) = 16/3
Therefore, the first 5 terms of the sequence are:
1/3, 2/3, 4/3, 8/3, 16/3.