Question

A geometric progression, for which the common ratio is positive, has a second term of 18 and a fourth term of 8. Find
1/ the first term and the common ratio of the progression.
2/ the sum of infinity of the progression.
Plz show me how to do it.

Answer 1

18=ar and 8=ar^3...
Now find r by dividing.. :D

Answer 2

\[T _{n}= ar^{n-1}\] is the equation...
So ,
\[T_{2}= ar^{2-1}\]\[18=ar----- 1.\] and
\[T_{4}=ar^{4-1}\]\[8=ar^{3}-----2.\]
Now divide 2 by 1..\[\frac{8=ar^{3}}{18=ar}\]\[r^{2}=\frac{4}{9}...r=\frac{2}{3}\]Now to find the first term substitute the value of r in 1.\[18=ar\]\[18=a*\frac{2}{3}\]\[ a=18*\frac{3}{2}\]\[a=27\]