Question

Scott decides to add running into an exercise routine and runs a total of 1 mile his first week he plans to double the number of miles he runs each week. a. Arithmetic or geometric. b. Recursive. c. explicit 

Answer 1

The question is an illustration of geometric progression.

• The recursive function is: $T_n = 2T_{n-1}$.
• The explicit function is: $T_n = 2^{n-1}$

From the question, we have:

$T_1= 1$ ---- the first week

$r = 2$ ---- The rate at which the distance increases each week.

When a sequence has a common ratio, the sequence is said to be a geometric sequence.

The Recursive function.

We have given that

$T_1= 1$ ---- the distance in the first week

The second week would be:

$T_2 = r \times T_1$

For the third week, the distance would be:

$T_3 = r \times T_2$

Express 2 as 3 - 1

$T_3 = r \times T_{3-1}$

Replace 3 with n, to get the distance for the nth week

$T_n = r \times T_{n-1}$

Substitute 2 for r

$T_n = 2 \times T_{n-1}$

$T_n = 2T_{n-1}$

Hence, the recursive function is: $T_n = 2T_{n-1}$

Explicit function

The nth term of a geometric sequence is:

$T_n = T_1 \times r^{n-1}$

Substitute values for $T_1$ and r.

$T_n = 1 \times 2^{n-1}$

$T_n = 2^{n-1}$

Hence, the explicit function is: $T_n = 2^{n-1}$

Read more about geometric sequence at:

https://brainly.com/question/18109692