Question

Write the recursive formula for the sequence 20, 60, 180,...Tn = 3 × Tn + 1Tn + 1 = Tn + 40Tn + 1 = 3 × TnTn + 1 = Tn + n × 40

Answer 1

`T_(n+1)\text{ = 3}* T_n`

Step-by-step explanation:

Here, we want to write the recursive formula

Looking at the sequence of numbers, we see that the succeeding term is 3 times the preceding term

Thus, we have the sequence as follows:

`\begin{gathered} T_n\text{ = 3}*\text{ T}_(n-1) \\ or\text{ } \\ T_(n+1)\text{ = 3}*\text{ T}_n \end{gathered}`

where:

Tn+1 is the term after Tn

and

Tn is the term after Tn-1