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An arithmetic sequence is given below.

-4, -10, -16, -22, ...
write an explicit formula for the Nth term aN.

1 Answer

4 votes

Answer:

an​=−6n+2

Explanation:

First, you need to identify the first term and the common difference of the sequence. The first term is the value of the first element, which is -4. The common difference is the amount that is added or subtracted to each term to get the next one, which is -6 in this case. You can find it by subtracting any two consecutive terms, such as -10 - (-4) = -6 or -16 - (-10) = -6.

Next, you need to use the standard explicit formula for an arithmetic sequence, which is:

an​=a1​+d(n−1)

where an​ is the Nth term, a1​ is the first term, d is the common difference, and n is any term number.

Finally, you need to substitute the values of a1​ and d that you found in the first step into the formula. This gives:

an​=−4+(−6)(n−1)

This is the explicit formula for the Nth term aN of the given arithmetic sequence. You can simplify it further by expanding and combining like terms:

an​=−4−6n+6

an​=−6n+2

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