Question

The general term for the sequence 3/4, 6/5, 9/6, 12/7, 15/8 is?

Answer 1

The numerators = 3n ( where n = sequence number of the term
The denominators = n + 3

Answer is 3n / (n + 3)

Answer 2

Sequence
`(3n)/(3+n)`.

Explanation:

Given : sequence 3/4, 6/5, 9/6, 12/7, 15/8 .

To find : The general term for the sequence.

Solution : We have given that 3/4, 6/5, 9/6, 12/7, 15/8 .

Here numerators are 3 , 6, 9 , 12, 15

Denominators are 4 ,5 , 6, 7, 8.

We can see in numerators all are multiple of 3

As, 3 × 1 , 3 × 2, 3 × 3 ...... etc

We can write it as : 3n

Denominator are 3 +1 , 3 +2 , 3 +3 ..........etc

We can write it as 3 +n

So , sequence become
`(3n)/(3+n)`

Therefore, sequence
`(3n)/(3+n)`.