Question

Find the first 10 terms of the sequence aₙ=1/aₙ−1​ and a₁​=25. The 9th term of the sequence is The 10th term of the sequence is

Answer 1

To find the first 10 terms of the sequence aₙ=1/aₙ−1 with a₁=25, we can use a recursive approach. The 9th term of the sequence is 25 and the 10th term of the sequence is 0.04.

Step-by-step explanation:

To find the first 10 terms of the sequence aₙ=1/aₙ−1 with a₁=25, we can use a recursive approach. We start with a₁=25, and then we can find the next term by substituting the previous term into the formula: a₂=1/a₁=1/25=0.04. We continue this process to find the first 10 terms:

1. a₁ = 25
2. a₂ = 1/25 = 0.04
3. a₃ = 1/a₂ = 1/0.04 = 25
4. a₄ = 1/a₃ = 1/25 = 0.04
5. a₅ = 1/a₄ = 1/0.04 = 25
6. a₆ = 1/a₅ = 1/25 = 0.04
7. a₇ = 1/a₆ = 1/0.04 = 25
8. a₈ = 1/a₇ = 1/25 = 0.04
9. a₉ = 1/a₈ = 1/0.04 = 25
10. a₁₀ = 1/a₉ = 1/25 = 0.04

So, the 9th term of the sequence is 25 and the 10th term of the sequence is also 0.04.