The sequence given:
This is an arithmetic sequence.
The first term (a1) is 7.
The common difference (d) between the terms is 10 - 7 =3, or 13 - 10 = 3.
To find the 33rd term of this sequence, we are going to use the nth term formula of an arithmetic sequence, shown below:
[tex]a_n=a_1+(n-1)d[/tex]Where
a_n is the nth term
a_1 is the first term
n is the number of the term
d is the common difference
Given,
a_1 = 7
d = 3
Let us find the 33rd term:
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ a_{33}=7+(33-1)3 \\ a_{33}=7+32(3) \\ a_{33}=7+96 \\ a_{33}=103 \end{gathered}[/tex]Thus, the 33rd term of this arithmetic sequence is 103.
Answer103
