Question

Find the recursive definition of the following sequence (Remember to define the first term t, the recursive rule to find tn,and the value n will start at.) 1, 6, 36, 216, 1296…..

Answer 1

Multiply to find the pattern which is 100

Answer 2

The answer is composed of the following two equations

$t_1 = 1$ and $t_n = 6*t_{n-1}$

both of these two equations combine to help form the full recursive definition

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Further explanation:

The terms are represented by the letter 't' for short. Since we have more than one term, and because we have only so many letters, this means we stick a number onto the 't' to help label multiple terms. We have t1 as the first term, t2 as the second, etc. The numbers are often show as subscripts like so $t_1, t_2, t_3, \ldots$

The first term of the list of numbers is 1, so $t_1 = 1$ is what we start with to help set up the recursive definition.

Once we have this starting point, we use it to get to the next term which is 6. This value is 6 times the first value. Therefore, the recursive step is $t_n = 6*t_{n-1}$ basically saying "multiply the (n-1)st term by 6 to get the nth term. Translation:  "whatever the current term is, multiply by 6 to get the next term".