The value of a = 5 ,and the value of b = 3
Using the formula for nth term = 2n² + an + b
When we put the value of n = 1
2 (1)² + a (1) + b = 10
2 + a + b = 10
a + b = 8 ...(Equation 1)
When we put the value of n = 2
2 (2)² + a( 2) + b = 21
8 + 2 (a) + b = 21
2 (a) + b = 13 ...(Equation 2)
(From equation 1)
a + b = 8
b = 8 - a ...(Equation 3)
(Putting value of b to equation 2)
2 (a) + 8 - a = 13
2(a) - a = 13 - 8 (By transposing)
a = 5
(Putting value of a to equation 3)
b = 8 - 5
b = 3