Question

Enter a recursive rule for the geometric sequence.

5, −10, 20, −40, ...

a1= an=

Answer 1

The recursive rule for the given geometric sequence is a1 = 5 and an = -2 * a(n-1) for n > 1, describing the initial term and the pattern of multiplying the previous term by -2.

Step-by-step explanation:

The sequence given is a geometric sequence where each term is multiplied by -2 to get the next term. To write a recursive rule for this sequence, we'll denote the first term as a1 and any term an in the sequence.

To establish the initial term, we have:

a1 = 5

For the recursive step, we multiply the previous term by -2 to find the next term, so we have:

an = -2 × an-1 for n > 1

Using this recursive rule, you can determine any term in the sequence by knowing its previous term.