Question

The first two terms of a sequence are a1 and a2=-1. Write the explicit rule if the sequence is arithmetic?

Answer 1

The explicit rule for an arithmetic sequence with the first two terms as a1 and a2=-1 is a_n = a1 - n + 1.

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. In this case, the first two terms of the sequence are a1 and a2, with a1 being the first term and a2 being -1. To find the explicit rule for this arithmetic sequence, we need to determine the common difference between consecutive terms.

We can find the common difference by subtracting the first term from the second term:

a2 - a1 = -1 - a1 = -1 - a1 = -1 - a1 = -2 - a1 = -1 - a1 = -1

Therefore, the common difference is -1. The explicit rule for an arithmetic sequence is given by:

a_n = a1 + (n-1)d

Substituting the values into the formula:

a_n = a1 + (n-1)(-1)

a_n = a1 - n + 1

So, the explicit rule for this arithmetic sequence is a_n = a1 - n + 1.