Question

What is the eighth value in the sequence 768, 384, 192, 96, ...?

Answer 1

6

Explanation:

Examine this sequence. What are the relations of these values?

Every time you increase 1 term in the sequence, divide by 2.

768/2 = 384

384/2 = 192

etc.

Write a geometric sequence formula.

`a_n = a*r^(^n^-^1^)`

A is the starting value (768), and r is the common ratio, or what the value is being multiplied by to get the next term. N is the term, where you can plug it in. For the eighth value, plug in 8 for n.

768 * ? = 384

1/2

r = 1/2

`a_n = 768 * 1/2^(^n^-^1^)`

For finding the eighth value, plug in 8 for n.'

`768 * 1/2^(^8^-^1^)`

`768 * 1/2^7`

768 * 0.0078125

6