Answer with Step-by-step explanation:
We are given a sequence as:
3.5, 13, 41.5, 127,...
we have to determine the pattern
13= 3.5×3+2.5
41.5= 13×3+2.5
127= 41.5×3+2.5
Hence, the sequence is defined as next term in the sequence is 3 times the previous term of the sequence plus 2.5
i.e. [tex]a_{n+1} =3a_{n} +2.5\ ;\ a_{1}=3.5[/tex]
Hence, Pattern is:
[tex]a_{n+1} =3a_{n} +2.5\ ;\ a_{1}=3.5[/tex]