## Lilmike234 one year ago 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?

1. campbell_st

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

2. campbell_st

and there are 2 possible answerz for r

3. lilmike234

Which are 1/7 and 3 right ?

4. campbell_st

|dw:1437106434841:dw| so then simplify the fraction |dw:1437106495856:dw|

5. campbell_st

so take thhe square root of both sides... of the equation and you'll get the 2 answers

6. lilmike234

3/4 and 1/4 ?

7. campbell_st

well you are halfway correct |dw:1437107382618:dw|