A sequence can be generated by using gn = 3(gn − 1), where g1 = 5 and n is a whole number greater than 1. What are the first five terms of the sequence?
To generate the first five terms of the sequence, we can use the given recursive formula.
Start with g₁ = 5.
To find g₂, we substitute n = 2 into the recursive formula:
g₂ = 3(g₂ - 1)
g₂ = 3(5 - 1)
g₂ = 3(4)
g₂ = 12
To find g₃, we substitute n = 3 into the recursive formula:
g₃ = 3(g₃ - 1)
g₃ = 3(12 - 1)
g₃ = 3(11)
g₃ = 33
To find g₄, we substitute n = 4 into the recursive formula:
g₄ = 3(g₄ - 1)
g₄ = 3(33 - 1)
g₄ = 3(32)
g₄ = 96
To find g₅, we substitute n = 5 into the recursive formula:
g₅ = 3(g₅ - 1)
g₅ = 3(96 - 1)
g₅ = 3(95)
g₅ = 285
Therefore, the first five terms of the sequence are:
5, 12, 33, 96, 285
To generate the first five terms of the sequence, we can use the given formula:
gn = 3(gn − 1)
Given g1 = 5, we can find the subsequent terms step-by-step:
g2 = 3(g1) = 3(5) = 15
g3 = 3(g2) = 3(15) = 45
g4 = 3(g3) = 3(45) = 135
g5 = 3(g4) = 3(135) = 405
Therefore, the first five terms of the sequence are 5, 15, 45, 135, and 405.