Question

How would you work this out step by step?

Answer 1

a = 6 , b = - 15

Explanation:

Substitute n = 3 and n = 6 into the nth term formula

a(3)² + 3b = 9 , that is

9a + 3b = 9 ( divide through by 3 )

3a + b = 3 → (1)

--------------------

a(6)² + 6b = 126 , that is

36a + 6b = 126 ( divide through by 6 )

6a + b = 21 → (2)

Subtract (1) from (2) term by term to eliminate b

3a + 0 = 18

3a = 18 ( divide both sides by 3 )

a = 6

Substitute a = 6 into (1) and solve for b

3(6) + b = 3

18 + b = 3 ( subtract 18 from both sides )

b = - 15

Answer 2

a=6

b= -15

Explanation:

third term --> n=3

a(3)^2 + b(3) =9

9a+3b=9

3(3a +b)=9

3a +b=9/3=3

3a + b=3 ------eqn1

sixth term n=6

a(6)^2 +6b =126

36a +6b=126

6(6a+b)=126

6a + b =126/6=21

6a + b=21----------eqn 2

eqn2 - eqn 1

(6a-3a) +(b-b) =21-3

3a=18

a=18/3=6

sub a= 6 into eqn2

6(6)+b=21

36 +b =21

b=21-36= -15