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

 

[Hurkyl]

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 I am wondering.. I don't think the way your thinking of works.. I forgot how to figure out the common ratio that's 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 don't 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 don't know how to figure them out
to make it more clear its:
-3=a₁r²
-192=a₁r⁸

 

[d_leet]

thats what i don't 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 don't 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]

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