Question

Find the 8th term of the following recursive sequence.

a subscript n equals a subscript n minus 1 end subscript plus a subscript n minus 2 end subscript; a subscript 1 equals 0 comma a subscript 2 equals 1; n greater or equal than 3

Answer 1

The 8th term of the recursive sequence is 13.

Step-by-step explanation:

The recursive sequence is defined as follows:

an = an-1 + an-2

The initial terms are a1 = 0 and a2 = 1.

To find the 8th term, we need to find the values of a3 through a8 using the recursive formula:

1. a3 = a2 + a1 = 1 + 0 = 1
2. a4 = a3 + a2 = 1 + 1 = 2
3. a5 = a4 + a3 = 2 + 1 = 3
4. a6 = a5 + a4 = 3 + 2 = 5
5. a7 = a6 + a5 = 5 + 3 = 8
6. a8 = a7 + a6 = 8 + 5 = 13

Therefore, the 8th term of the sequence is 13.