Answer:
see explanation
Step-by-step explanation:
(a)
The common difference (d) in an arithmetic sequence is
d = [tex]a_{2}[/tex] - [tex]a_{1}[/tex] = 24 - 2 = 22
To obtain the next term in the sequence add 22 to the previous term
[tex]a_{4}[/tex] = 46 + 22 = 68
[tex]a_{5}[/tex] = 68 + 22 = 90
[tex]a_{6}[/tex] = 90 + 22 = 112
--------------------------------------------------
(b)
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a + (n - 1)d
where a is the first term and d the common difference
here a = 2 and d = 22, hence
[tex]a_{n}[/tex] = 2 + 22(n - 1) = 2 + 22n - 22 = 22n - 20 ← n th term formula
---------------------------------------------------------------------
(c)
Using the n th term formula
[tex]a_{35}[/tex] = (22 × 35) - 20 = 770 - 20 = 750
