Here are the first five terms of a sequence. 30, 29, 27, 24. 20, ... Find, in terms of n, an expression for the nth term of the sequence.How to...

The first 5 terms of the sequence are 30,
29,27,24,20.

So a1 = 30, a2 = 29, a3 = 27, a4 = 24, a5 =
20.

a2-a1 = -1, a3-a2 = -2, a4-a3 = -3, a5-a4 = -4....,
an-an-1 = n-1.

Therefore an = a1 - 1 -2 -3 - ... -(n-1) =
a1- {1+2+3+..(n-1)} = a1-n(n-1)/2.

an =
30-n(n-1)/2. 

Therefore, an = 30-n(n-1)/2 is
the expression for the nth term in terms of
n.

Tally:

a1 = 30 -(1)(0)/2 =
30

a2 = 30 -2(2-1)/2 = 29

a3 =
30 - 3(3-1)/2 = 30 -3 = 27

a4 = 30 - 4(4-1)/2 =  30 - 6 =
24

a5 = 30 -5(5-1)/2 = 30 -10 = 20.