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Decide if the sequence is arithmetic, geomtric, or neither. After you determine the type of sequence find the term given below. 2, 8, 32, 128 . . . Find a subscript 10 space

Sagot :

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]