Question

if tn=an^2+ bn+ cand T1=10,T2=19 and T3=32find value of a,b,c​

Answer 1

Answer:

a = 2, b= 3, c = 5

Step-by-step explanation:

tn = an^2 + bn + c

t1

$t1 = a( {1)}^{2} + b1 + c = 10 \\ = a + b + c = 10 \\ t2 = a {(2)}^{2} + b(2) + c = 19 \\ = 4a + 2b + c = 19 \\ t3 = a {(3)}^{2} + b(3) + c = 32 \\ = 9a + 3b + c = 32 \\ \\ t2 - t1 \\ 3a + b = 9 \: \: \: \: \: equ(1) \\ \\ t3 - t2 \\ 5a + b = 13 \: \: \: \: equ(2) \\ \\ equ \: (2) - (1) \\ 2a = 4 \\ a = \frac{4}{2} = 2$

substitute a = 2 in equ (1)

3(2) + b = 9

6 + b = 9

b = 9 - 6 = 3

substitute a = 2, b = 3 in t1

a + b + c = 10

2 + 3 + c = 10

5 + c = 10

c = 10 - 5

c = 5

a = 2, b = 3, c = 5

hope you get your answer