Question

Shaunta is developing a recursive formula to represent an arithmetic sequence in which 5 is added to each term to determine each successive term. Which formula could represent her sequence?

Answer 1

Answer:

$a_{n+1} = a_n + 5$                

Step-by-step explanation:

We are given the following in the question:

An arithmetic sequence where 5 is added to every term.

Thus, common difference, d = 5

Let the first term be

$a = a_0$

Then, $n^{th}$ term of an arithmetic sequence is given by:

$a_n = a_0 + (n-1)d$

Putting values, we get,

$a_n = a_0 + (n-1)5\\a_n = a_0 + 5n - 5\\a_{n+1} = a_0 + (n+1-1)5\\a_{n+1} = a_0 + (n-1)5 + 5\\a_{n+1} = a_n + 5$

is the required recursive relation for arithmetic progression.

Answer 2

Answer:

a f(n + 1) = f(n) + 5

Step-by-step explanation: