Answer:
The first four terms are 3,9,27,81
Step-by-step explanation:
Step :-1
Given first term of sequence is [tex]a_{1} = 3[/tex]
Given 'n' t h term is [tex]a_{n} = 3 a_{n-1}[/tex] .............(1)
here we put n = 2 in equation (1)
[tex]a_{2} = 3a_{2-1}[/tex]
[tex]a_{2} = 3 a_{1}[/tex] ..............2
put [tex]a_{1} = 3[/tex] in equation (2)
[tex]a_{2} = 3(3)[/tex]
[tex]a_{2} = 9[/tex]
put n=3 in equation (1)
[tex]a_{3} = 3 a_{3-1}[/tex]
[tex]a_{3} = 3a_{2}[/tex]
[tex]a_{3} = 3 (9) = 27[/tex]
put n= 4 in equation (1)
[tex]a_{4} = 3 a_{4-1}[/tex]
[tex]a_{4} = 3 a_{3}[/tex]
[tex]a_{4} = 3(27) = 81[/tex]
The first four terms of the sequence is
3 , 9, 27 , 81 ....this is geometric sequence
a =3 and ratio term is r =3
