Answered

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Find the explicit formula for a 1 =-4,a n =a n-1 +9,n>=2

Sagot :

Given:

[tex]a_1=-4[/tex] and [tex]a_n=a_{n-1}+9[/tex] where [tex]n\geq 2[/tex].

To find:

The explicit formula for the given recursive formula.

Solution:

We know that recursive formula of an AP is:

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

Where, d is the common difference.

We have,

[tex]a_n=a_{n-1}+9[/tex]

Here, d=9.

The first term of the AP is [tex]a_1=-4[/tex].

The explicit formula for an AP is:

[tex]a_n=a_1+(n-1)d[/tex]

Substituting [tex]a_1=-4[/tex] and [tex]d=9[/tex], we get

[tex]a_n=-4+(n-1)9[/tex]

[tex]a_n=-4+9n-9[/tex]

[tex]a_n=-13+9n[/tex]

Therefore, the required explicit formula for the given sequence is [tex]a_n=-13+9n[/tex].

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