Question

Write a recursive formula and an explicit formula for the following arithmetic sequence. 14,17,20,23,26

Answer 1

The recursive formula is $a_{1}$ = 14;  $a_{n}$ = $a_{n-1}$ + 3

The explicit formula is $a_{n}=3n+11$

Step-by-step explanation:

The recursive formula of the nth term of the arithmetic sequence is

$a_{1}$ = first term;  $a_{n}$ = $a_{n-1}$ + d, where

• $a_{1}$ is the first term in the sequence
• $a_{n}$ is the nth term in the sequence  
• $a_{n-1}$ is the term before the nth term  
• n is the term number
• d is the common difference.

The explicit formula of the nth term of the arithmetic sequence is

$a_{n}=a+(n-1)d$ , where

• $a_{n}$ is the nth term in the sequence
• a is the first term
• n is the term number
• d is the common difference

∵ The arithmetic sequence is 14, 17, 20, 23, 26

∴ The first term is 14

∵ 17 - 14 = 3

∴ The common difference is 3

∵ The recursive formula is $a_{1}$ = first term;  $a_{n}$ = $a_{n-1}$ + d

∵ $a_{1}$ = 14

∵ d = 3

∴ $a_{1}$ = 14;  $a_{n}$ = $a_{n-1}$ + 3

The recursive formula is $a_{1}$ = 14;  $a_{n}$ = $a_{n-1}$ + 3

∵ The explicit formula is $a_{n}=a+(n-1)d$

∵ a = 14

∵ d = 3

∴ $a_{n}=14+(n-1)3$

- Simplify the right hand side

∴ $a_{n}=14+3n-3$

- Add like terms

∴ $a_{n}=3n+11$

The explicit formula is $a_{n}=3n+11$

Learn more:

You can learn more about the sequences in brainly.com/question/7221312

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