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

Geometric sequence

`a_(10) = 524288`

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 = (a_2)/(a_1)` --- common ratio

`r = (8)/(2)=4`

`r = (a_3)/(a_2)`

`r = (32)/(8) = 4`

`r = (a_4)/(a_3)`

`r = (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`