Question

How do I write an equation for this sequence and determine the 8th term: 7, 7.5, 7.75, 7.875... ?

Answer 1

There are I believe two types of sequences: arithmetic & geometric. These sequences all have formulas that will help me determine the 8th term.

Answer 2

Write the decimal part as a fraction and look for a pattern.

Answer 3

First 0.5 is added, then 0.25 then 0.125 ..... It is a progression of adding powers of 5 with decimals.

Answer 4

Equation is:

\[ f(n)=8 - \left(\frac12\right)^{n - 1} \]

The 8th term is 7.99219.