Question

Each sequence below gives an explicit formula. Write the first five terms of each sequence. Then, write a recursive

formula for the sequence.
b. an = (1 / 2) n−1 for n ≥ 1

Answer 1

Answer: Hello there!

we have the equation a(n) = (1/2)n - 1 for n ≥ 1

First we need the first five terms:

a(1) = (1/2)*1 - 1 = -1/2

a(2) = (1/2)*2 - 1 = 0

a(3) = (1/2)*3 - 1 = 1/2

a(4) = (1/2)*4 - 1 = 1

a(5) = (1/2)*5 - 1 = 3/2

then we can see that each term is 1/2 bigger than the previous one, then a recursive relation can be written as:

a(n) = a(n-1) + 1/2

where n ≥ 2, and a(1) = -1/2