Answer:
[tex]a_n=28-6n[/tex]
Step-by-step explanation:
Formula for arithmetic sequence: [tex]a_n=a+(n-1)d[/tex]
Given:
- [tex]a_6=-8[/tex]
- [tex]a_{15}=-62[/tex]
[tex]a_6=a+5d=-8[/tex]
[tex]a_{15}=a+14d=-62[/tex]
[tex]a_{15}-a_6\implies 9d=-54[/tex]
[tex]\implies d=-6[/tex]
Substituting found value for d into one of the equations and solving for a:
[tex]a_6=a+(5 \times -6)=-8[/tex]
[tex]\implies a=22[/tex]
[tex]\implies a_n=22-6(n-1)[/tex]
[tex]\implies a_n=28-6n[/tex]
