Answer:
[tex]S_3=35[/tex]
Step-by-step explanation:
Given: [tex]S_1=3\,,S_n=7(S_{n-1}-2)[/tex]
To find: [tex]S_3[/tex]
Solution:
First find [tex]S_2[/tex]
Put [tex]n=2[/tex] in [tex]S_n=7(S_{n-1}-2)[/tex]
[tex]S_2=7(S_{2-1}-2)\\S_2=7(S_1-2)[/tex]
Put [tex]S_1=3[/tex]
[tex]S_2=7(3-2)=7[/tex]
Now find [tex]S_3[/tex]
Put [tex]n=3[/tex] in [tex]S_n=7(S_{n-1}-2)[/tex]
[tex]S_3=7(S_{3-1}-2)\\S_3=7(S_{2}-2)[/tex]
Put [tex]S_2=7[/tex]
[tex]S_3=7[(7)-2]=7(5)=35[/tex]
