Answered

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Write an recursive formula for An, the nth term of the sequence
5, -2, -9,

Sagot :

Given:

The given sequence is:

[tex]5,-2,-9,...[/tex]

To find:

The recursive formula for [tex]a_n[/tex], the nth term of the sequence.

Solution:

We have,

[tex]5,-2,-9,...[/tex]

Here, the first term is 5.

[tex]-2-5=-7[/tex]

[tex]-9-(-2)=-9+2[/tex]

[tex]-9-(-2)=-7[/tex]

The common difference is -7.

The recursive formula for the nth term of the sequence is

[tex]a_n=a_{n-1}+d[/tex]

Where, [tex]d[/tex] is the common difference.

Putting [tex]d=-7[/tex] in the above formula, we get

[tex]a_n=a_{n-1}+(-7)[/tex]

[tex]a_n=a_{n-1}-7[/tex]

Therefore, the recursive formula for the nth term of the sequence is [tex]a_n=a_{n-1}-7[/tex].

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