Question

A sequence is defined recursively. Find the first seven terms of the sequence. aₙ=√3aₙ₋₁, a₁=√3

Answer 1

The first seven terms of the recursive sequence are: √3, 3, 3√3, 9, 9√3, 27, 27√3.

Step-by-step explanation:

The recursive sequence is defined by the formula an = √3an-1 where a1 = √3. To find the first seven terms of the sequence, we can substitute the values of n = 1, 2, 3, 4, 5, 6, and 7 into the formula:

1. a1 = √3
2. a2 = √3(√3) = 3
3. a3 = √3(3) = 3√3
4. a4 = √3(3√3) = 9
5. a5 = √3(9) = 9√3
6. a6 = √3(9√3) = 27
7. a7 = √3(27) = 27√3

Therefore, the first seven terms of the sequence are: √3, 3, 3√3, 9, 9√3, 27, 27√3.