Answer:
B . [tex]\frac{3 n}{n+3}[/tex]
Step-by-step explanation:
Arithmetic sequence:-
Step1:
Given sequence is [tex]\frac{3}{4} ,\frac{6}{5} ,\frac{9}{6} ,\frac{12}{7} ,\frac{15}{8}[/tex]
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
[tex]t_{n} =a+(n-1)d[/tex]
now substitute a =3 and d=3
[tex]t_{n} = 3+(n-1)3 = 3+3 n-3=3n[/tex]
Step2:-
Above sequence taking denominator
4,5,6,7,8...
here a=4 and d=1
[tex]t_{n} =a+(n-1)d[/tex]
[tex]t_{n} =4+(n-1)1[/tex]
[tex]t_{n}=3+n[/tex]
Final answer is the general term of given sequence is
[tex]t_{n} = \frac{3n}{3+n}[/tex]
