We need to find how many terms are in the given sequence:
Which starts with 3,7,11 until 123.
Now, looking at the sequence, it has a common difference:
7-3 = 4
11-7= 4
So, the common difference is 4.
Then,
3,7,11,11+4=15, 15+4= 19,19+4= 23 ............. 123
So, if the sequence goes on,we use the next formula:
[tex]T_n=a+\left(n+1\right)d[/tex]
Where d=common difference
Tn = the n term
n= total terms
Replacing:
[tex]\begin{gathered} 123=3+\left(n-1\right)4 \\ Solve\text{ for n} \\ 123-3=\left(n-1\right)4 \\ 120=4n-4 \\ 120+4=4n \\ Then \\ n=\frac{124}{4} \end{gathered}[/tex]
Therefore, the total number for the sequence is 31
