How to find indicated number in geometric sequence with two given numbers?

I need help on the following problems and any of these will do. I am doing a review for my upcoming finals and I need help. T_T





Find an indicated number of geometric means between the two give numbers.





1. two between 1 and 64


2. one between 5 and 45


3. three between 5 and 80


4. one between 10 and 20





Thanks in advance! Tips and pointers will do.How to find indicated number in geometric sequence with two given numbers?
(I will be using the letters in caps because it is difficult to show subscripts...)


Basically, you need to use the formula An= A1(R)^(n-1)


1. Since you know that A1= 1, and that A4=64, you can find R.


64= 1(R)3


R=4


Once you find R, you can do the sequence.


1, 4, 16, 64.





2. A1=5, A3=45


45= 5(R)2


9=R^2


R= +/- 3 %26lt;-- if it is the square, fourth, sixth, and so on root, you must remember that it can be positive or negative.


5, -15, 45 or 5,15,45





3. A1=5, A5=80


80= 5(R)^4


16= R^4


R= +/- 2


5, 10, 20, 40, 80 or 5,-10,20,-40,80





4. A1=10, A3=20


20= 10R^2


2=R^2


R= +/- Square root of 2


10, 10square root 2, 20


10, -10square root 2, 20How to find indicated number in geometric sequence with two given numbers?
Tn = a r^(n 鈥?1)


use this formula


T1 = 1and T4 = 64


T4 = T1 r^(4 鈥?1) ---------- T1 is first term and r is common ratio


64 = r鲁


r = 4


T2 = T1 脳 r = 4


T3 = T1 脳 r虏 = 16


series is 1, 4, 16, 64


Tn = a r^(n 鈥?1)





I hope you can solve others.


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