Answered

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The recursive formula of an arithmetic sequence is described below A1 = 19, an = an-1 + 6Write the explicit equation of this arithmetic sequence given the recursive formula

Sagot :

We have the sequence:

[tex]\begin{gathered} a_1=19 \\ a_n=a_{n-1}+6 \end{gathered}[/tex]

We can derive the explicit equation by looking at the first terms of the sequence and deriving the pattern:

[tex]\begin{gathered} a_1=19 \\ a_2=a_1+6=19+6 \\ a_2=a_2+6=(a_1+6)+6=a_1+2\cdot6=19+2\cdot6 \\ a_3=a_2+6=(a_1+2\cdot6)+6=a_1+3\cdot6=19+3\cdot6 \end{gathered}[/tex]

We then can generalize to:

[tex]a_n=19+n\cdot6=19+6n[/tex]

Answer: the explicit formula is a_n=19+6n

[tex]a_n=19+6n[/tex]

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