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Mathematical patterns: Write the first five terms of a sequence. Don’t make your sequence too simple. Write both an explicit formula and a recursive formula for a general term in the sequence. Explain in detail how you found both formulas.



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Solution

Step-by-step explanation:

We are to write the first five terms of a sequence, along with the explicit and recursive formula for the general term of the sequence.

Let the first five terms of a sequence be 5, 10, 20, 40 and 80

These terms are taken from a geometric sequence with first term

[tex]a_15,r=2[/tex]

first term a = 5

common ratio r = 2

Therefore, we have

[tex]\begin{gathered} a_2=a_1\times r \\ a_3=a_2\times r \end{gathered}[/tex]

Therefore, the recursive formula is

[tex]\begin{gathered} a_{n+1}=2a_n \\ a_1=5 \end{gathered}[/tex]

And explicit formula is

[tex]a_n=a_1r^{n-1}[/tex]

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