Answer to Question #266087 in Algebra for Good heart

Question

The fourth term of geometric sequence is 8 and the sixth term is 32. Find the possible common ratios

Answer 1

The n^th term of a geometric sequence with "a" as the first term and "r" as the common ratio

n^th $=$ ar ^n-1

$4^{th}$ term ;

ar³ $=8$ ........(i)

$6^{th}$ term ;

ar⁵ $=32$ ..........(ii)

dividing equation (ii) by equation (i)

$\frac{ar^5}{ar^3}=\frac{32}{8}\implies$ r² $=4$

$\therefore\>r=2$ or $-2$