Answer:
Hence, the possible missing number is:
250 or -250
Step-by-step explanation:
We have to find the missing term in the given geometric sequence.
1250 , _ , 50 , ...
Let a denote the first term of the sequence and r denote the common ratio of the geometric sequence then the geometric sequence is defined as:
[tex]a,ar,ar^2,ar^3,......[/tex]
Let:
[tex]a=1250, ar, ar^2=50[/tex]
so that means:
[tex]1250\times r^2=50\\\\r^2=\dfrac{50}{1250}\\\\r^2=\dfrac{1}{25}\\\\r=\pm \dfrac{1}{5}[/tex]
so, the possible missing number is calculated at two values of r.
Hence, the missing number is:
[tex]ar=1250\times \dfrac{1}{5}\\\\ar=250[/tex] or
[tex]ar=1250\times \dfrac{-1}{5}\\\\ar=-250[/tex]
