Answer:
sixth term a₆ = 42
Explanation:
given the nth term formula
= an² + bn ( we require to find a and b )
given a₂ = - 2 , then
a(- 2)² + b( 2) = - 2 , that is
4a + 2b = - 2 → (1)
given a₄ = 12 , then
a(4)² + b(4) = 12 , that is
16a + 4b = 12 → (2)
multiplying (1) by - 2 and adding to (2) will eliminate b
- 8a - 4b = 4 → (3)
add (2) and (3) term by term to eliminate b
8a + 0 = 16
8a = 16 ( divide both sides by 8 )
a = 2
substitute a = 2 into (1) and solve for b
4(2) + 2b = - 2
8 + 2b = - 2 ( subtract 8 from both sides )
2b = - 10 ( divide both sides by 2 )
b = - 5
then the nth term formula is
= 2n² - 5n , so
a₆ = 2(6)² - 5(6) = 2(36) - 30 = 72 - 30 = 42