Answer:
The value of [tex]a_{4}=15[/tex]
Step-by-step explanation:
Given that [tex]a_{1}=6[/tex] and [tex]a_{n}=a_{n-1}+3[/tex]
Given sequence is of the form arithmetic sequence
For arithmetic sequence the sequence is [tex]a_{1},a_{2},a_{3},...[/tex]
The nth term is of the form [tex]a_{n}=a_{n-1}+d[/tex]
Here [tex]a_{1}=6[/tex] and [tex]a_{n}=a_{n-1}+3[/tex]
from this the common differnce is 3.
Therefore d=3
To find [tex]a_{2}[/tex], [tex]a_{3}[/tex] , [tex]a_{4}[/tex]
[tex]a_{n}=a_{n-1}+d[/tex]
put n=2 and d=3 we get
[tex]a_{2}=a_{2-1}+3[/tex]
[tex]a_{2}=a_{1}+3[/tex]
[tex]a_{2}=6+3[/tex] (here [tex]a_{1}=6[/tex] )
Therefore [tex]a_{2}=9[/tex]
[tex]a_{n}=a_{n-1}+d[/tex]
put n=3 and d=3 we get
[tex]a_{3}=a_{3-1}+3[/tex]
[tex]a_{3}=a_{2}+3[/tex]
[tex]a_{3}=9+3[/tex] (here [tex]a_{2}=9[/tex] )
Therefore [tex]a_{3}=12[/tex]
[tex]a_{n}=a_{n-1}+d[/tex]
put n=4 and d=3 we get
[tex]a_{4}=a_{4-1}+3[/tex]
[tex]a_{4}=a_{3}+3[/tex]
[tex]a_{4}=12+3[/tex] (here [tex]a_{3}=12[/tex] )
Therefore [tex]a_{4}=15[/tex]
Therefore the sequence is 6,9,12,15,...
Therefore the value of [tex]a_{4}=15[/tex]
