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
`(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 =
`(3)/(4) / (7)/(8)`

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

Solving the above gives
`(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 =
`(7)/(8)` x
`(6)/(7)` ⁿ⁻¹

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