Question

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

Answer 1

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 \(d = 1\).

Answer 2

wrong

Answer 3

My apologies for the mistake, let's correct it:

Given (9, 1), (5, 2), and (1, 3), let's calculate the common difference:

From (9, 1) to (5, 2):
d = (2 - 1) / (5 - 9) = 1 / -4 = -1/4

From (5, 2) to (1, 3):
d = (3 - 2) / (1 - 5) = 1 / -4 = -1/4

Therefore, the common difference is -1/4.

Now, let's calculate the fourth term:

Using the formula for nth term:
a_n = a_1 + (n-1)d

a_1 = 9 (from the first term)

n = 4

d = -1/4

a_4 = 9 + (4-1)(-1/4)
a_4 = 9 - 3/4
a_4 = 36/4 - 3/4
a_4 = 33/4 = 8.25

Therefore, the fourth term is 8.25.

Now, let's calculate the fifth term:

a_5 = 9 + (5-1)(-1/4)
a_5 = 9 - 4(1/4)
a_5 = 9 - 1
a_5 = 8

Therefore, the fifth term is 8.

In summary, the common difference is -1/4, the fourth term (a_4) is 8.25, and the fifth term (a_5) is 8.