Geometric, Arithmetic, or neither? What are the next 2 terms of this sequence.

Question

40,10,5/2,5/8

 

 

 

 

 

please help

Answer 1

Each term is 1/4 of the preceding term...

 

10 = 40(1/4)

 

5/2 = 1/4(10)

 

5/8 = 1/2(5/4)

 

This is a geometric sequence

Answer 2

10/40 = 1/4

 

(5/2)/10 = 1/4

 

(5/8)/(5/2) = 1/4, etc

 

The sequence is geometric with common ratio r = 1/4 and first term 40

 

So, the nth term a_n is given by the formula a_n = a₁r^n-1

 

Therefore, a₅ = 40(1/4)⁴ = 40/256 = 5/32

 

               a₆ = 40(1/4)⁵ = 40/1024 = 5/128