Question

15, 11, 7, 3, -1, ... explicit formula and recursive formula

Answer 1

Recursive formula is: $a_n = a_{n-1} -4$

Explicit formula is: $a_n = 19-4n$

Step-by-step explanation:

Given sequence is:

15,11,7,3,-1

Here

$a_1 = 15\\a_2 = 11\\a_3 = 7$

First of all, we have to find the common difference

Common difference is the difference between consecutive terms of an arithmetic sequence

So,

$d = a_2-a_1 = 11-15 = -4\\d = a_3-a_2 = 7-11 = -4$

Recursive Formula:

A recursive formula is used to find the next term of an arithmetic sequence using previous term and common difference

General form of recursive formula for a given common difference d is:

$a_n = a_{n-1} + d$

Putting the value of d

$a_n = a_{n-1} -4$

Explicit Formula:

The explicit formula is given by:

$a_n = a_1 + (n-1)d$

Putting the first term and common difference

$a_n = 15 + (n-1)(-4)\\a_n = 15 -4n+4\\a_n = 19-4n$

Hence,

Recursive formula is: $a_n = a_{n-1} -4$

Explicit formula is: $a_n = 19-4n$

Keywords: Arithmetic sequence, common difference

Learn more about arithmetic sequence at:

• brainly.com/question/726990
• brainly.com/question/725998

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