Thread: sequences and series geometric

If the third and ninth temr of a geometric series with a positive common ratio are -3 and -192 repectively, determine the value of the first term a

what formula would I use to answer this kind of question? how would I do this question?
thanks for your help! I just need someone who can explain to me hwo I would approach this sort of question! thanks a lot!

Originally Posted by bobbluecow

If the third and ninth temr of a geometric series with a positive common ratio are -3 and -192 repectively, determine the value of the first term a

what formula would I use to answer this kind of question? how would I do this question?
thanks for your help! I just need someone who can explain to me hwo I would approach this sort of question! thanks a lot!

We know that,
Let a_1 be denoted by 'a' (first terms) then,
a_3=r^2 a
And,
a_9=r^8 a
Thus,
r^8 a=-192
r^2 a=-3
Divide two equations,
r^6=64=2^6
Thus,
r=2

The third term is,
-3=2^2 a
Thus,
a=-3/4