Question

A geometric sequence is shown below 2,-6,18,-54,162,... part A: what a recursive relationship for this sequence. Explain how you determined your answer part B: write an explicit formula for this sequence

Answer 1

Answer:

• a_n = -3a_(n-1); a_1 = 2
• a_n = 2·(-3)^(n-1)

Step-by-step explanation:

A) The problem statement tells you it is a geometric sequence, so you know each term is some multiple of the one before. The first terms of the sequence are given, so you know the first term. The common ratio (the multiplier of interest) is the ratio of the second term to the first (or any term to the one before), -6/2 = -3.

So, the recursive definition is ...

... a_1 = 2

... a_n = -3·a_(n-1)

B) The explicit formula is, in general, ...

... a_n = a_1 · r^(n -1)

where r is the common ratio and a_1 is the first term. Filling in the known values, this is ...

... a_n = 2·(-3)^(n-1)