When a sequence has a common difference, then the sequence is arithmetic
The next two terms are -5 and -9
The sequence is given as: 11, 7, 3, -1
The above sequence have a common difference.
This is calculated by subtracting a term from the next term.
i.e.
[tex]\mathbf{d = T_2 - T_1 = T_3 - T_2 = T_{n+1} - T_n}[/tex]
So, we have:
[tex]\mathbf{d = 7 - 11}[/tex]
[tex]\mathbf{d = -4}[/tex]
The nth term of an arithmetic sequence is:
[tex]\mathbf{T_n = T_1 + (n - 1)d}[/tex]
So, we have:
[tex]\mathbf{T_n = 11 + (n - 1)(-4)}[/tex]
[tex]\mathbf{T_n = 11 -4n +4}[/tex]
Evaluate like terms
[tex]\mathbf{T_n = 15 -4n }[/tex]
The next two terms are the 5th and the 6th terms.
So, we have:
[tex]\mathbf{T_5 = 15 -4 \times 5 = -5}[/tex]
[tex]\mathbf{T_6 = 15 -4 \times 6 = -9}[/tex]
Hence, the next two terms are -5 and -9
Read more about arithmetic sequence at:
https://brainly.com/question/18109692
