Instructions: Select the appropriate explicit rule for the given sequence. Sequence: −14,86,186,286,…

The given sequence is -14, 86, 186, 286, ...

Step 1: Identify the common difference The difference between consecutive terms is 100 (86 - (-14) = 100, 186 - 86 = 100, 286 - 186 = 100).

Step 2: Write the explicit rule Since the common difference is 100, the explicit rule for the nth term of the sequence is an = a1 + (n-1)d, where a1 is the first term and d is the common difference.

Step 3: Substitute the values into the formula So, the explicit rule for this sequence is an = -14 + (n-1)100.

Therefore, the explicit rule for the given sequence is an = -14 + 100n - 100, which simplifies to an = 100n - 114.