Answer:
9, 13, 17, 21, 25, 29
Step-by-step explanation:
Since there is an equal increase of the same amount, the sequence is arithmetic with n th term
Substituting a = 9 and d = 4 into the n th term expression
[tex]a_{n}[/tex] = 9 + 4(n - 1) = 9 + 4n - 4 = 4n + 5
[tex]a_{n}[/tex] = a + (n - 1)d
where a is the first term and d the common difference
The third term and sixth term are therefore
a + 2d = 17 → (1)
a + 5d = 29 → (2)
Subtract (1) from (2) term by term, eliminating a, that is
3d = 12 ( divide both sides by 3 )
d = 4
Substitute d = 4 into either of the 2 equations and solve for a
Substituting into (1)
a + 2(4) = 17
a + 8 = 17 ( subtract 8 from both sides )
a = 9
Thus the first term is 9 and the common difference d = 4
The sequence of terms is therefore
9, 13, 17, 21, 25, 29
Substituting a = 9 and d = 4 into the n th term expression
[tex]a_{n}[/tex] = 9 + 4(n - 1) = 9 + 4n - 4 = 4n + 5
