Answered

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2,-2,-6,-10,-14, ...how do I go about finding the explicit formula?

Sagot :

According to the given sequence, the difference is -4, because it's decreasing with that difference: 2-2 = -2; -2-4 = -6; and so on.

To find the explicit formula, we use the arithmetic sequence formula.

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

Replacing all the given information, we have.

[tex]\begin{gathered} a_n=2+(n-1)\cdot(-4) \\ a_n=2-4n+4 \\ a_n=6-4n \end{gathered}[/tex]

This explicit formula we can also express as

[tex]f(n)=6-4n[/tex]

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