Question

Find the sixth term of a geometric sequence with t5 = 24 and t8 = 3.

Answer 1

ar^5 = 24 and ar^8 = 3.
Divide second by first:
\[\frac{ ar^8 }{ ar^5 }= \frac{ 3 }{ 24 }\]
The a's cancel and we reduce the r's:
\[r^3 = \frac{ 1 }{ 8 }\]
so r=1/2
Use ar^5 = 24 with our r=1/2 to get a=768.
To find 6th term input a=768 and r=1/2 into ar^n with n=6:
\[768 \times (\frac{ 1 }{ 2 }) ^6 =12\]

Answer 2

Not sure if I made it clear enough that the n'th term of a geometric sequence is given by \[ar^n\] where a is the first term, r is the common ratio and n is the term number.