Question

1 over 3 , 3 over 4 ,4 over 7 , 7 over 11, 11over 8 .... (i)one termof this sequence is p over q . Find the term of p and q , the next term in this sequence . Find the 6th term of this sequence 1).... 2).....

Answer 1

Next term will be the 6th term i.e. a₆ will be:

• a₆ = 14/11

Here:

• p = numerator = 14

• q = denominator = 11

Explanation:

Given the sequence

`(1)/(3),\:(3)/(4),\:(4)/(7),\:(7)/(11),\:(11)/(8),...`

First of all the terms of the sequence are in p/q form, where p is the numerator and q is the denominator.

As the fifth term of the sequence is:

a₅ = 11/8

From the given sequence it is clear that the numerator is changing by 3 units and the denominator is also changing by 3 units.

Thus,

The next term will be the 6th term i.e. a₆ will be:

• a₆ = 14/11

Here:

• p = numerator = 14

• q = denominator = 11