Question

I need help finding the common ratio and general term equation

Answer 1

From the given graph, we see that

1st term = 32

2nd term = 24

3rd term = 18

So, the geometric sequence is 32, 24, 18...

The general form of the geometric sequence is given by

`a_n=a_1(r)^(n-1)`

Where aₙ is the nth term, a₁ is the first term and r is the common ratio.

The common ratio is basically the ratio of any two consecutive terms.

r = 18/24 = 0.75

r = 24/32 = 0.75

So, the common ratio is 0.75

The first term is 32

So, the general equation of the sequence becomes

`a_n=32(0.75)^(n-1)`