Question

Find the nth term in the sequence 7/8, 3/4, 9/14

Answer 1

Given parameters:

Terms of the sequence  = 7/8 , 3/4 , 9/14

From terms, we know that our first term is  $\frac{7}{8}$

We need find either of the common difference or the common ratio of this sequence.

For this, the common ratio is applicable.

  Common ratio  = $\frac{3}{4} / \frac{7}{8}$

 This is the factor by which when we multiply the subsequent terms with results into them;

     Solving the above gives $\frac{6}{7}$

The common ratio is 6/7.

To find the nth of this sequence we apply the formula below;

            A$_{n}$  = Arⁿ⁻¹

Aₙ is the term we are looking for

A is the first term of the sequence

r is the common ratio

n is the position of the term

  So for any nth term in this sequence;

         Aₙ   = $\frac{7}{8}$ x $\frac{6}{7}$ ⁿ⁻¹

We can use the above solution to find any term in the sequence.