Question

Write a recursive rule for the sequence. 243, 81, 27, 9, 3, ..

Answer 1

Answer: Answer is AR^n-1 (A multiplied by R {raised to the power of n minus 1} )

Step-by-step explanation: The above sequence is a geometric progression or geometric sequence. Each term is derived or calculated by multiplying with a common ratio.

The common ratio is not given but is normally calculated as each term divided by the previous term. That is, R (common ratio) is

81/243, or 27/81, or 9/27...,

So our common ratio here is ⅓

Hence, the Geometric progression now has its recursive rule written as

AR^n-1

Where A = 2, R = ⅓ and n is the nth term