Question

The graph represents an arithmetic sequence. Find the common difference, d, the fourth term, a4, the fifth term, a5, of the arithmetic sequence.
The graph shows points as, (1, 3), (5, 2) and (9,1).

Answer 1

To find the common difference, d, we can find the difference between consecutive terms:

d = 2 - 3 = -1
d = 1 - 2 = -1

Therefore, the common difference, d, is -1.

To find the fourth term, a4, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n-1)d

a4 = 3 + (4-1)(-1)
a4 = 3 - 3
a4 = 0

Therefore, the fourth term, a4, is 0.

To find the fifth term, a5, we use the same formula:

a5 = 3 + (5-1)(-1)
a5 = 3 - 4
a5 = -1

Therefore, the fifth term, a5, is -1.