Answer:
see explanation
Step-by-step explanation:
the sequence is linear, that is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
given a₈ = 18 and a₁₂ = 26 , then
a₁ + 7d = 18 → (1)
a₁ + 11d = 26 → (2)
subtract (1) from (2) term by term to eliminate a₁
4d = 8 ( divide both sides by 4 )
d = 2
substitute d = 2 into (1) and solve for a₁
a₁ + 7(2) = 18
a₁ + 14 = 18 ( subtract 14 from both sides )
a₁ = 4
then
a₂₀ = 4 + (19 × 2) = 4 + 38 = 42
