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