Question

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

Answer 1

Answer:

Geometric sequence

$a_{10} = 524288$

Step-by-step explanation:

Given

$a: 2,8,32,128...$

Solving (1): The type of sequence

To check for arithmetic sequence:

$d = a_2 - a_1$ --- common difference

$d = 8 - 2 = 6$

$d =a_3 - a_2$

$d =32-8=24$

Both values of d are not the same; Hence, the sequence is not arithmetic

To check for geometric sequence:

$r = \frac{a_2}{a_1}$ --- common ratio

$r = \frac{8}{2}=4$

$r = \frac{a_3}{a_2}$

$r = \frac{32}{8} = 4$

$r = \frac{a_4}{a_3}$

$r = \frac{128}{32} = 4$

All values of r are the same.

Hence, it is a geometric sequence

Solving (2): Find $a_{10$

For a geometric sequence;

$a_n = a_1 * r^{n-1$

$a_{10} = 2 * 4^{10-1$

$a_{10} = 2 * 4^9$

$a_{10} = 524288$