we are given
1.11, 2.54, 3.97, 5.40, ...
we can see that
first term is 1.11
now, we can find common difference
[tex] d=2.54-1.11 [/tex]
[tex] d=1.43 [/tex]
now, we can find second difference
[tex] d=3.97-2.54 [/tex]
[tex] d=1.43 [/tex]
we can see that
differences are same
so, this is arithematic sequence
now, we can find it's nth term
[tex] a_n=a_1+(n-1)d [/tex]
[tex] a_n=1.11+(n-1)*1.43 [/tex]
now, we can simplify it
and we get
[tex] a_n=1.43n-0.32 [/tex]............Answer
