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Answer:
Geometric sequence
[tex]a_{10} = 524288[/tex]
Step-by-step explanation:
Given
[tex]a: 2,8,32,128...[/tex]
Solving (1): The type of sequence
To check for arithmetic sequence:
[tex]d = a_2 - a_1[/tex] --- common difference
[tex]d = 8 - 2 = 6[/tex]
[tex]d =a_3 - a_2[/tex]
[tex]d =32-8=24[/tex]
Both values of d are not the same; Hence, the sequence is not arithmetic
To check for geometric sequence:
[tex]r = \frac{a_2}{a_1}[/tex] --- common ratio
[tex]r = \frac{8}{2}=4[/tex]
[tex]r = \frac{a_3}{a_2}[/tex]
[tex]r = \frac{32}{8} = 4[/tex]
[tex]r = \frac{a_4}{a_3}[/tex]
[tex]r = \frac{128}{32} = 4[/tex]
All values of r are the same.
Hence, it is a geometric sequence
Solving (2): Find [tex]a_{10[/tex]
For a geometric sequence;
[tex]a_n = a_1 * r^{n-1[/tex]
[tex]a_{10} = 2 * 4^{10-1[/tex]
[tex]a_{10} = 2 * 4^9[/tex]
[tex]a_{10} = 524288[/tex]