Answer:
[tex]a_{20} = 1/1048576[/tex]
Step-by-step explanation:
Given
[tex]Sequence: -1/2;1/4;-1/8;1/16[/tex]
Required
Determine [tex]a_{20[/tex]
Since it is a geometric sequence, first we need to calculate the common ratio (r)
[tex]r = \frac{a_2}{a_1}[/tex]
From the sequence:
[tex]a_2 = 1/4[/tex]
[tex]a_1 = -1/2[/tex]
[tex]a_1[/tex] is the same as [tex]a[/tex]
So:
[tex]r = \frac{a_2}{a_1}[/tex]
[tex]r = \frac{1/4}{-1/2}[/tex]
[tex]r = -1/2[/tex]
[tex]a_{20[/tex] is then calculated as:
[tex]a_n = ar^{n-1}[/tex]
Where
[tex]n = 20[/tex]
[tex]a_{20} = ar^{20-1}[/tex]
[tex]a_{20} = ar^{19}[/tex]
[tex]a_{20} = (-1/2) * (-1/2)^{19}[/tex]
Apply law of indices
[tex]a_{20} = (-1/2)^{1+19}[/tex]
[tex]a_{20} = (-1/2)^{20}[/tex]
Evaluate the exponent
[tex]a_{20} = 1/1048576[/tex]
