Question

Write an explicit formula for an,the nth term of the sequence 72,12,2​

Answer 1

`n _(th) = n _(1) {r}^(n - 1) \\ n _(th) = 72 * 12 {}^((n - 1)) \\ n _(th) = 72 * ( {12}^(n) .12^(-1)) \\ n _(th) = 6 × {12}^(n)`

Answer 2

`a_n = 432 \cdot \left((1)/(6)\right)^n` OR
`a_n = 72 \cdot \left((1)/(6)\right)^(n-1)`

Explanation:

The first term is 72, and each term is equal to the previous term multiplied by 1/6. This yields the expression
`a_n = 72 \cdot \left((1)/(6)\right)^(n-1)`, which is equivalent to
`a_n = 432 \cdot \left((1)/(6)\right)^n`.