Chapter 11.3, Problem 38WE

To determine

To calculate:

The formula for $n^{th}$ term for the following sequence which is neither arithmetic nor geometric:

  $\frac{1}{2},\frac{2}{5},\frac{3}{8},\frac{4}{11},\mathrm{.....}$

Answer to Problem 38WE

The formula for $n^{th}$ term is $\frac{n}{3n-1}$ .

Explanation of Solution

Given information:

  $\frac{1}{2},\frac{2}{5},\frac{3}{8},\frac{4}{11},\mathrm{.....}$

Calculation:

Here, already given that the sequence $\frac{1}{2},\frac{2}{5},\frac{3}{8},\frac{4}{11},\mathrm{.....}$ is neither arithmetic nor geometric.

Check the numerator of series is power of index and the denominator is three times of power of index minus one.

Hence, the formula becomes for the $n^{th}$ term:

  $\frac{1}{2},\frac{2}{5},\frac{3}{8},\frac{4}{11},\mathrm{.....}=\frac{n}{3n-1}$