Given:
[tex]a_1=10\text{ and }a_n=a_{n-1}+1.[/tex][tex]\text{ Substitutting n=2 in }a_n=a_{n-1}+1,\text{ we get}[/tex][tex]a_2=a_{2-1}+1[/tex][tex]a_2=a_1+1[/tex][tex]\text{Substitute }a_1=10,\text{ we get }[/tex][tex]a_2=10+1[/tex][tex]\text{ We get }a_2=11.[/tex][tex]\text{ Substitutting n=3 in }a_n=a_{n-1}+1,\text{ we get}[/tex][tex]a_3=a_{3-1}+1[/tex][tex]a_3=a_2+1[/tex][tex]\text{Substitute }a_2=11,\text{ we get }[/tex][tex]a_3=11_{}+1[/tex][tex]\text{ We get }a_3=12.[/tex][tex]\text{ Substitutting n=4 in }a_n=a_{n-1}+1,\text{ we get}[/tex][tex]a_4=a_{4-1}+1[/tex][tex]a_4=a_3+1[/tex][tex]\text{Substitute }a_3=12,\text{ we get }[/tex][tex]a_4=12+1[/tex][tex]a_4=13[/tex][tex]\text{ Hence the required value is }a_4=13.[/tex]
The answer is
[tex]a_4=13[/tex]
