# Geometric sequence, determining the value of the first term

#### tug187

question - if the 3rd and 9th term of a geometric series with a positive common ratio are -3 and -192 respectively, determine the value fo the first term, a.

I kno we using
a_n=a_1r^n-1

From that i got this :

-3 = a_1r^2
-192 = a_1r^8

But I dont kno how I can solve for r or a_1... I also don't know if I even did it right

#### Hurkyl

Staff Emeritus
Gold Member
Well, you have two equations in two unknowns, don't you? How do you generally solve such things?

#### tug187

Well, you have two equations in two unknowns, don't you? How do you generally solve such things?
thats what im wondering.. I dont think the way your thinking of works.. I forgot how to figure out the common ratio thats all i really need to know

#### roger

You need to solve the equations you wrote down to get r=

-3 = a_1r^2
-192 = a_1r^8

#### tug187

You need to solve the equations you wrote down to get r=

-3 = a_1r^2
-192 = a_1r^8
thats what i dont understand, on other questions i got the common ratio easily by using the term before it but these 2 terms r not after each other so i dont know how to figure them out
to make it more clear its:
-3=a1r2
-192=a1r8

#### d_leet

thats what i dont understand, on other questions i got the common ratio easily by using the term before it but these 2 terms r not after each other so i dont know how to figure them out
to make it more clear its:
-3=a1r2
-192=a1r8
What happens if you divide the second equation by the first?

#### tug187

What happens if you divide the second equation by the first?
64 = r6 ?
26 = r6
r = 2?

anyone kno if this is right?

#### Hurkyl

Staff Emeritus
Gold Member
Well, if you computed a_1 too, you could check for yourself to see if it's right!

#### tug187

Well, if you computed a_1 too, you could check for yourself to see if it's right!
Ok...

ifwe know that term 3 is -3,
a3 = a1*r^3-1
-3 = a1*2^2
-3 = 4*a1
-3/4 = a1

should be right