Question

A recursive function is defined by: an = 2a n - 1 with a0 = 1

Find the value of a3

Answer 1

a_n = 2a_n-1 where a₁ = 1

tells me your sequence starts with 1, and each new term is double the
one before it, that is .....
1, 2, 4, 8, ....

Answer 2

Thank you

Answer 3

[AI-generated answer — Explain Bot]

To find the value of a3 using the given recursive function, we can use the following steps:

1. Start with the initial condition: a0 = 1
2. Plug in the value of n = 1 into the recursive formula:
a1 = 2a1 - 1
Simplify: a1 = 2a0
a1 = 2(1)
a1 = 2

3. Repeat the process for n = 2:
a2 = 2a2 - 1
Simplify: a2 = 2a1
a2 = 2(2)
a2 = 4

4. Finally, calculate a3:
a3 = 2a3 - 1
Simplify: a3 = 2a2
a3 = 2(4)
a3 = 8

Thus, the value of a3 is 8.