Question

What is the first term of the geometric sequence whose fifth term is 1/24 and tenth term is 1/768

Answer 1

\[The\ n ^{th}\ term\ is\ ar ^{n-1}\]
So we can set up two equations as follows:
\[\frac{1}{24}=ar ^{4}............(1)\]
\[\frac{1}{768}=ar ^{9}...........(2)\]
Now we need to solve these equations to find the first term a and the common ratio r.
Do you follow so far?

Answer 2

Let the first term be a, and the common ratio be r. Then \[1/24=a r^{4}\] and \[1/768=ar ^{9}\]. Hence you may divide to obtain\[r^{5}=ar ^{9}/ar ^{4}=\frac{ \frac{ 1 }{ 768 } }{ \frac{ 1 }{ 24 } }= \frac{ 1}{ 32 }\] which implies that r=1/2. Go back to the equation for 1/24 and solve to obtain a=2/3.

Answer 3

so whats the answer

Answer 4

@kropot72

Answer 5

@tesa12345 Can you follow the solution by @francisgcm?

Answer 6

no. im really confused

Answer 7

@Blank

Answer 8

What part of the solution do you have trouble with? The answer is given in the post by @francisgcm

Answer 9

is it a half?

Answer 10

wait no, its 2/3 right?

Answer 11

Correct.