The first four terms of a sequence are 500, 300, 180, and 108. Determine the value of the 16th term

Question

How does sequencing work because I really don't understand it

 

Answer 1

As Mark said:

 

In this case the numbers have a common ratio:
300/500 = 180/300 = 108/180 = 0.6
 
a_n = a₁(r)^n-1       explicit form a geometric sequence

 

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however, there was a typo when he wrote the equation

to actually calculate the value of a₁₆ because r = 0.6, not 0.06

 

a₁₆ = 500(0.6)¹⁵

Answer 2

A sequence can be arithmetic, every pair of terms has the same difference

A sequence can be geometric, every pair of terms has the same quotient (ratio)

In this case the numbers have a common ratio:

300/500 = 180/300 = 108/180 = 0.6

 

a_n = a₁(r)^n-1       explicit form a geometric sequence

a₁₆ = 500(0.06)¹⁵

 

Can you calculate a₁₆?