Question

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

Answer 1

Answer:

B . $\frac{3 n}{n+3}$

Step-by-step explanation:

Arithmetic sequence:-

Step1:

Given sequence is $\frac{3}{4} ,\frac{6}{5} ,\frac{9}{6} ,\frac{12}{7} ,\frac{15}{8}$

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

$t_{n} = \frac{3n}{3+n}$