Answer:
56
Step-by-step explanation:
The n th term of an AP is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₆ = 17 and a₁₃ = 38, then
a₁ + 5d = 17 → (1)
a₁ + 12d = 38 → (2)
Subtract (1) from (2) term by term to eliminate a₁
7d = 21 ( divide both sides by 7 )
d = 3
Substitute d = 3 into (1) and evaluate for a₁
a₁ + 5(3) = 17
a₁ + 15 = 17 ( subtract 15 from both sides )
a₁ = 2
Thus
[tex]a_{19}[/tex] = 2 + (18 × 3) = 2 + 54 = 56
