ANSWER
A)
[tex]a_ {10}= 87[/tex]
B)
[tex]a_ {75}=9(75)-3 = 672[/tex]
C)
[tex]a_n=9n - 3[/tex]
EXPLANATION
The terms of the sequence are,
6,15,24,33,42,...
The common difference is
[tex]d=15-6 = 9[/tex]
The first term is
[tex]a_1=6[/tex]
C)
The nth term of an arithmetic sequence is
[tex]a_n= a_1+d(n-1)[/tex]
[tex]a_n= 6+9(n-1)[/tex]
[tex]a_n= 6+9n - 9[/tex]
[tex]a_n=9n - 3[/tex]
A) To find the tenth term, we put n=10 into the formula,
[tex]a_ {10}= 9(10) - 3 = 87[/tex]
B) To find the 75th term, we put n=75 into the formula,
[tex]a_ {75}=9(75)-3 = 672[/tex]
