Question

Write an explicit furmula for the question below
40 points!!!!!!!!!!!!!

Answer 1

aₙ = a₁ . 5⁽ⁿ⁻¹⁾

Explanation:

The first term in the sequence is a₁ = 6.

a₂ = 30. a₃ = 150.

We see that each consecutive term is multiplies by 5 to arrive at the next term.

That is: a₂ = 30 = a₁ .
`$ 5^(2 - 1)  = 5 $` = 6.5 = 30.

Similarly, a₃ = 150 = 6
`$ * $`
`$ 5^(3 - 1) = 5^2 = 25 $`

Generalizing this, we have:

aₙ = a₁ .
`$ 5^(n - 1) $`

This is called the recursive formula of the sequence.