Answer:
a = 256; r = [tex]$ \frac{1}{2} $[/tex]
Step-by-step explanation:
The general form of the geometric sequence is:
a, ar, ar², ar³, . . .
where 'a' is the first term of the sequence;
'r' is the common difference.
Fourth term of the sequence = ar³ = 32
Sixth term of the sequence = ar⁵ = 8
Dividing both the equations, we get:
[tex]$ \frac{ar^5}{ar^3} = \frac{8}{32} $[/tex]
⇒ r² = [tex]$ \frac{1}{4} $[/tex]
⇒ r = [tex]$ \frac{1}{2} $[/tex]
Therefore, we get a = 32 X 8
a = 256
The first term of the sequence is 256 and the common difference is [tex]$ \frac{1}{2} $[/tex].
Hence, the answer.
