Question

Write a recursive rule for this sequence:
4, 12, 36, 108, 324.....

Answer 1

it's being multiplied by 3 each time

Answer 2

Looks like it's a normal geometric sequence.

Answer 3

We have the common ratio = 3 and first term = 4.\[T_n = T_1\times r^{n-1 } \]The most you can do here is substitute \(T_1\) with \(4\). That leaves you with\[T_n = 4r^{n - 1} \]

Answer 4

T is used conventionally to determine the triangular numbers; A is used as a generic ... not that it matters ;)

Answer 5

Sorry, Amistre. My apologies :)

Answer 6

the rule should have 2 parts; defining inital terms and defining the relation between successive terms

Answer 7

getting the first term to a 1 or a zero is usually helpful in picking out a pattern