Question

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

Answer 1

A geometric sequence is where you keep multiplying by a certain ratio
lets suppose the "r" be the ratio
1/24=5th term
1/24* r = 6th term
1/24*r*r=7th term
1/24 * r* r*r=8th term
...
1/24*r^5=10th term=1/768
we can solve for r

Answer 2

Then to figure out the first term, now that we know the 5th term and know the r value.
You know that to go from Term 1 to Term 5, we would multiply Term 1 by r a total of 4 times.
x* r^4=1/24
and we can find x, since we already found r previously. X is our first term.

Answer 3

wat ?

Answer 4

0_e

Answer 5

What?

Answer 6

i have no clue what u typed or what your talking about _-_

Answer 7

Maybe it's best you did some review before attempting to solve these problems then.

Answer 8

Would you like me to refer you to some content/teaching material, that would be helpful to you?

Answer 9

\[\frac{ 2 }{ 3 }\]

Answer 10

?

Answer 11

What did you find your "r" to be

Answer 12

1/24*r^5=10th term=1/768
1/24*r^4=1/768 <--- solve for r first.

Answer 13

fifth term is 1/24 and tenth is 1/768
r^5 = (1/768) / ( 1/24) = 1/32
r = 1/2
a*r^4 = 1/24
the first term: 2/3

Answer 14

Correct! You got it! It is indeed 2/3.

Answer 15

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)

. 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.