Question

Arithmetic sequences are ___ function. Geometric sequences are ____ functions. An arithmetic sequence is a sequence of numbers in which the common ____ (d) is ____ to preceding term. A geometric sequence is a sequence of numbers in which the common ____ (r) is _____ by the previous term. Both arithmetic and geometric sequences have _____ and recursive 3, 9, 27, 81 .... is a ____ sequence where common ____ is -2, -4, -6, -8, ... is an ____ sequence where common ____ is 40, 45, 50, 55, 60, ... is an ___ sequence common ___ is −1, 6, −36, 216, ... is a ____ sequence where common _____ is

Answer 1

Arithmetic sequences are **linear** functions. Geometric sequences are **exponential** functions. An arithmetic sequence is a sequence of numbers in which the common **difference** (d) is **added** to the preceding term. A geometric sequence is a sequence of numbers in which the common **ratio** (r) is **multiplied** by the previous term. Both arithmetic and geometric sequences have **explicit** and **recursive** definitions.

The sequence 3, 9, 27, 81, ... is a **geometric** sequence where the common **ratio** is **3**. The sequence -2, -4, -6, -8, ... is an **arithmetic** sequence where the common **difference** is **-2**. The sequence 40, 45, 50, 55, 60, ... is an **arithmetic** sequence where the common **difference** is **5**. The sequence -1, 6, -36, 216, ... is a **geometric** sequence where the common **ratio** is **-6**.