The 63rd term is [tex]-\frac{247}{16}[/tex] if it is an arithmetic sequence.
The 63rd term is [tex]2.385\times 10^{28}[/tex] if it is an geometric sequence.
An arithmetic sequence has the characteristic that the difference between two consecutive elements is the same, that is to say:
[tex]a_{i+1}-a_{i} = r[/tex] (1)
The expression that represents the elements of the arithmetic sequence is presented below:
[tex]a(n) = a_{1} + r\cdot (n-1)[/tex] (2)
Where:
If we know that [tex]a_{1} = \frac{1}{16}[/tex], [tex]a_{2} = -\frac{3}{16}[/tex] and [tex]n = 63[/tex], then the 63rd term of the arithmetic sequence:
[tex]r = -\frac{3}{16}-\frac{1}{16}[/tex]
[tex]r = -\frac{1}{4}[/tex]
[tex]a(63) = \frac{1}{16}-\frac{1}{4}\cdot (63-1)[/tex]
[tex]a(63) = -\frac{247}{16}[/tex]
The 63rd term is [tex]-\frac{247}{16}[/tex] if it is an arithmetic sequence.
An geometric sequence has the characteristic that the ratio between two consecutive elements is the same, that is to say:
[tex]\frac{a_{i+1}}{a_{i}} = r[/tex] (3)
The expression that represents the elements of the geometric sequence is presented below:
[tex]a(n) = a_{1}\cdot r^{n-1}[/tex] (4)
Where:
If we know that [tex]a_{1} = \frac{1}{16}[/tex], [tex]a_{2} = -\frac{3}{16}[/tex] and [tex]n = 63[/tex], then the 63rd term of the arithmetic sequence:
[tex]r = \frac{-\frac{3}{16} }{\frac{1}{16} }[/tex]
[tex]r = -3[/tex]
[tex]a (63) = \left(\frac{1}{16} \right)\cdot (-3)^{63-1}[/tex]
[tex]a(63) = 2.385\times 10^{28}[/tex]
The 63rd term is [tex]2.385\times 10^{28}[/tex] if it is an geometric sequence.
We kindly invite to see this question on geometric sequence: https://brainly.com/question/11266123
