Answer:
Option 2nd is correct
[tex]-\frac{1}{3}[/tex]
Step-by-step explanation:
The nth term for the arithmetic sequence is given by:
[tex]a_n = a+(n-1)d[/tex]
where,
[tex]a_1[/tex] is the first term
d is the common difference
n is the number of terms.
As per the statement:
From the given graph:
At n =1
[tex]a_1 =4[/tex]
At n =4
[tex]a_4=3[/tex]
Using the nth term formula for the arithmetic sequence:
[tex]a_4 = a_1+3d[/tex]
Substitute the given values we have;
[tex]3 = 4+3d[/tex]
Subtract 4 from both sides we have;
[tex]-1 = 3d[/tex]
Divide both sides by 3 we have;
[tex]-\frac{1}{3} =d[/tex]
or
[tex]d =-\frac{1}{3}[/tex]
Therefore, the common difference for the given sequence as shown is, [tex]-\frac{1}{3}[/tex]
