Question

The second term in a geometric sequence is 20. The fourth term in the same sequence is 45/4 or 11.25. What is the common ratio in this sequence?

Answer 1

well a term in a geometric sequence is found using

\[a_{n} = a \times r^{n -1}\]

and you know the 2nd term

\[20 = a \times r^{2 -1} ~~~or~~~20 = a \times r\]

and he 4th term

\[\frac{45}{4} = a \times r^3\]

which can be written as

\[\frac{45}{4} = a \times r \times r^2\]

make the substitution for the 2nd term

\[\frac{45}{4} = 20 \times r^2\]

now you can solve for r

Answer 2

and there are 2 possible answerz for r

Answer 3

Which are 1/7 and 3 right ?

Answer 4

so then simplify the fraction