Question

Find the series in which
5th term is 22/16 and 4th term is -4​

Answer 1

The series is given as follows;

`-(161)/(8) , \ -(59)/(4) , \ -(75)/(8), \ -4, \ (22)/(16) ......`

Explanation:

Assuming the series is an arithmetic progression, (AP), series, we have

The nth term of the desired series = a + (n - 1)×d

Where;

a = The first term

n = The position of the term in the series

d = The common difference

Given that the 5th term = 22/16 and the 4th term = -4, we have;

d = The difference between consecutive terms = Difference between the 5th term and the 4th term

∴ d = 22/16 - (-4) = 43/8 = 5.375

22/16 = a + (5 - 1)×5.375

∴ a = 22/16 - 4×5.375 = -20.625

The series is therefore;

`-(161)/(8) , \ -(59)/(4) , \ -(75)/(8), \ -4, \ (22)/(16) ......`