Answer: The explicit rule for the sequence will be
[tex]a_n=15.5-2.5n[/tex]
Step-by-step explanation:
Since we have given that
[tex]13,10.5,8,5.5,3,0.5.....[/tex]
Here,
a = first term = 13
d = common difference
[tex]a_2-a_1 = 10.5-13=-2.5[/tex]
Since it forms an A.P. ;
[tex]a_n=a+(n-1)d\\\\a_n=13+(n-1)(-2.5)\\\\a_n=13-2.5n+2.5\\\\a_n=15.5-2.5n[/tex]
Hence, the explicit rule for the sequence will be
[tex]a_n=15.5-2.5n[/tex]
