Question

Determine if the sequence is algebraic or geometric, and find the common difference or ratio.

х 1 2 3 4
f(x) 3 9 27 81
O Algebraic, common difference = 3
Algebraic, common difference = 6
O Geometric, common ratio = 3
O Geometric, common ratio = 6

Answer 1

The sequence f(x) = 3, 9, 27, 81 is a geometric sequence with a common ratio of 3, as each term is obtained by multiplying the previous term by 3.

Step-by-step explanation:

For the sequence given as f(x) = 3, 9, 27, 81, we need to determine whether it is an algebraic sequence with a common difference or a geometric sequence with a common ratio. By comparing each consecutive term, we observe that each term is obtained by multiplying the previous term by the same number. This indicates that our sequence is geometric. The common ratio, r, can be found by dividing any term by the preceding term.

For example:

• 9 ÷ 3 = 3
• 27 ÷ 9 = 3
• 81 ÷ 27 = 3

Hence, the common ratio, r, is 3. Therefore, the sequence is a geometric sequence with a common ratio of 3.