Question

These are the first six terms of a sequence with a1= -7:

Answer 1

The recursive formula for this sequence is $a_{1}$ = -7;  $a_{n}$ = $a_{n-1}$ + 10

Step-by-step explanation:

The recursive formula of the arithmetic sequence is:

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

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

∵ The sequence is -7 , 3 , 13  , 23 , 33 , 43 , ........

∵ 3 - (-7) = 3 + 7 = 10

∵ 13 - 3 = 10

∵ 23 - 13 = 10

- There is a constant difference 10 between the consecutive terms

∴ The sequence is an arithmetic sequence

∵ The first term is -7

∴ $a_{1}$ = 7

∵ The common difference is 10

∴ d = 10

- Substitute in the formula above $a_{1}$ by -7 and d by 10

∴ $a_{1}$ = -7;  $a_{n}$ = $a_{n-1}$ + 10

To check the formula find the second term

∵ n = 2

∴ $a_{1}$ = -7;  $n_{2}$ = $n_{2-1}$ + 10

∴  $n_{2}$ = $n_{1}$ + 10

∵ $n_{1}$  = -7

∴ $n_{2}$ = -7 + 10 = 3 which is right

The recursive formula for this sequence is $a_{1}$ = -7;  $a_{n}$ = $a_{n-1}$ + 10

Learn more:

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

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