Question

Write the recursive formula for each sequence. Then write the next two terms.

an =an−1 ×(−3)

a. -162, 486

b. 162, -486

c. -162, -486

d. 162, 486

Answer 1

The recursive formula for the sequence an = an-1 × (-3) leads to alternating signs for each term. When applied to the given sequences, the next two terms can be calculated based on the most recent term being multiplied by -3.

Step-by-step explanation:

The recursive formula for the given sequence an = an-1 × (-3) can be applied to each of the sequences provided:

• (a) For the sequence -162, 486, the next term a3 = 486 × (-3) = -1458, and a4 = -1458 × (-3) = 4374.

• (b) For the sequence 162, -486, the next term a3 = -486 × (-3) = 1458, and a4 = 1458 × (-3) = -4374.

• (c) For the sequence -162, -486, the next term a3 = -486 × (-3) = 1458, and a4 = 1458 × (-3) = -4374.

• (d) For the sequence 162, 486, the next term a3 = 486 × (-3) = -1458, and a4 = -1458 × (-3) = 4374.

Note that each sequence alternates signs due to the multiplication by -3 in the recursive formula.