Question

A geometric sequence has a4=4 and a5=7 . What is a1 ?

Answer 1

please help... I want to say a1= -5 but i think i did the arithmetic sequence way and not the geometric sequence way

Answer 2

Do you know how to write the general term of a GP

Answer 3

no

Answer 4

Its written like this

\[T_n=ar^{n-1}\]
\(T_n\) =\(n^{th} \) term
a= 1st term
r=common ratio

Answer 5

But i don't have the common ratio nor do i have a1

Answer 6

You can get the common ratio by dividing two consecutive terms

Answer 7

For example
Common ratio=(2nd term) /(1st term)

Answer 8

but i only have the 4th term and 5th term
do i use those??

Answer 9

The 4th and 5th terms are consecutive

You get the 5th term when you multiply the 4th with common ratio

Dividing the 5th term by the 4th one will give you the common ratio

Answer 10

so 1.75 would be r???

Answer 11

Yes

Answer 12

Next we need to find "a"

Answer 13

would a3 be 2.29 or did i do that wrong??

Answer 14

Correct! :)

Answer 15

See that equation i wrote above

When you plug \(T_n\) =4, n=4 and r=1.75 you can find a

Answer 16

a is our 1st term tho and thats what we need to find

Answer 17

btw you can also find a( or you can call it a1) by same way you found a3

Answer 18

i got a1=0.75
but just just kept dividing the number i got by 1.75 until i got to a1...i didn't use the formula i still don't understand it

Answer 19

Thats correct but your approach might not be suitable if the question asked to find a53 cuz then it will be too much calculation

I can help u understand the fornula

Answer 20

ok please explain

Answer 21

Suppose the 1st term is a and common ratio is r

You get the a2 by multiplying a with r right

So a2 will be - > ar

Similarly you can get ae by multiplying r and a2

So a3 =ar^2

a4=ar^3
a5=ar^4
a6=ar^5
a7=ar^6
a8=ar^7

See a pattern forming here?
The \(n^{th} \) term is given by
\(T_n = ar^{n - 1}\)

Answer 22

That not ae

Its supposed to be *a3

Answer 23

a4=ar^3 = ar^(4-1)
a5=ar^4 =ar^(5-1)
a6=ar^5 =ar^(6-1)
a7=ar^6 =ar^(7-1)
a8=ar^7 =ar^(8-1)

Answer 24

okay but this one started at a4 wouldn't i have to work backwards to get to a1

Answer 25

You found r and you already know the value of a4

And you also know that
\[a_n=ar^(n-1)\]
Btw \[T_n\] and \[a_n\] are the same thing

For a4 - n will be 4
r is 1.75 and a4 is 4

Soo \[4=a(1.75)^{4-1}\] solve this to get a

Answer 26

i understand it thank you and what if i wanted a2 instead of a1? what would i had plug in differently??
(im not asking you to work the whole thing out just plug it in for me)