Question

What is the nth term of 5.5 7 8.5 10 11.5

Answer 1

  my answer to you would be that for this kind of a sequence, there is a fixed way of finding the nth term value 
let's get these basics straight first: 
1) Un= the nth term value 
for eg. U1 = 1st term value 
2) a = first term 
3) d = difference 
Ok now the first step to finding the nth term is finding the constant difference 
in the example that you gave the constant difference is 1.5 
ie 1.5 is being added on each time 
now the fixed rule for finding the nth term is : 
Un = a + d(n-1) 
why? 
because let's take a common example of a linear sequence, a sequence with a constant first term ( so called because it forms a line when drawn in a graph): 
first term is a so, 
a, a+d, a+2d, a+3d......a(n-1)d 
(because the coefficient of d is one less than the term number) 
so putting this into your q: 
a = 5.5 
d=1.5 
Un=a + d (n-1) 
Un=5.5 + 1.5(n-1) 
Un=5.5 + 1.5n - 1.5 
Un=4+ 1.5n 
there you go it works... 
for other types like quadratic cubic and geometric progression, its a totally different story