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tiny-mole [99]
4 years ago
9

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

Mathematics
1 answer:
monitta4 years ago
4 0

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

<u>Recursive Formula:</u>

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

<u>Explicit Formula:</u>

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

#LearnwithBrainly

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