Answer:
2 and 420
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 a₃ = 6 and a₁₆ = 32 , then
a₁ + 2d = 6 → (1)
a₁ + 15d = 32 → (2)
Subtract (1) from (2) term by term
13d = 26 ( divide both sides by 13 )
d = 2
Substitute d = 2 into (1) for corresponding value of a₁
a₁ + 2(2) = 6
a₁ + 4 = 6 ( subtract 4 from both sides )
a₁ = 2
The sum of n terms of an AP is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ] , thus
[tex]S_{20}[/tex] = [tex]\frac{20}{2}[/tex] [(2 × 2) + (19 × 2) ]
= 10(4 + 38) = 10 × 42 = 420
