Question

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

A. n+3/n+1

B. 3n/3+n

C. 3n/n+1

Answer 1

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

Explanation:

Arithmetic sequence:-

Step1:

Given sequence is
`(3)/(4) ,(6)/(5) ,(9)/(6) ,(12)/(7) ,(15)/(8)`

Above sequence taking numerator terms

3,6,9,12,15 are in arithmetic progression

First term a= 3 and difference d = 3

now n t h term of given sequence is

`t_(n) =a+(n-1)d`

now substitute a =3 and d=3

`t_(n) = 3+(n-1)3 = 3+3 n-3=3n`

Step2:-

Above sequence taking denominator

4,5,6,7,8...

here a=4 and d=1

`t_(n) =a+(n-1)d`

`t_(n) =4+(n-1)1`

`t_(n)=3+n`

Final answer is the general term of given sequence is

`t_(n) = (3n)/(3+n)`