Answer:
see explanation
Step-by-step explanation:
The n th term of a geometric sequence is
[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]
where a is the first term and r the common ratio
Given [tex]a_{12}[/tex] = [tex]\frac{1}{32}[/tex] and r = [tex]\frac{1}{2}[/tex], then
a [tex](\frac{1}{2}) ^{11}[/tex] = [tex]\frac{1}{32}[/tex], that is
[tex]\frac{a}{2^{11} }[/tex] = [tex]\frac{1}{32}[/tex]
[tex]\frac{a}{2048}[/tex] = [tex]\frac{1}{32}[/tex] ( cross- multiply )
32a = 2048 ( divide both sides by 32 )
a = 64 ← first term
Thus the explicit formula is
[tex]a_{n}[/tex] = 64 [tex](\frac{1}{2}) ^{n-1}[/tex]
