To find the common difference of an arithmetic sequence given three consecutive terms, we can use the formula:
\(d = a2 - a1 = a3 - a2\)
Using the given points:
For (9, 1) and (5, 2):
\(d = 2 - 1 = 1\)
For (5, 2) and (1, 3):
\(d = 3 - 2 = 1\)
So, the common difference is \(d = 1\).
To find the fourth term, we can use the formula for the nth term of an arithmetic sequence:
\(a_n = a_1 + (n-1)d\)
Plugging in the values for a1, d, and n = 4:
\(a4 = 1 + (4-1)1 = 1 + 3 = 4\)
So, the fourth term is \(a4 = 4\).
To find the fifth term, we can use the same formula:
Plugging in the values for a1, d, and n = 5:
\(a5 = 1 + (5-1)1 = 1 + 4 = 5\)
So, the fifth term is \(a5 = 5\), and the common difference is \(d = 1\).