Question

A sequence is generated by the formula Mn =an^2 + bn+c, where a , b and c are
constants. If M.1 = 4, M2 = 10 and M3 = 18, find the values of a b and c.​

Answer 1

Answer:

The values of  a , b and c

a=1

b=3

c=0

Step-by-step explanation:

Given:

$M_n =a\,n^2+b\,n+c$

For n=1,

$M_1=a(1)^2+b(1)+c$

$4=a+b+c$

$a+b+c=4$..........(1)

For n=2,

$M_2=a(2)^2+b(2)+c$

$10=4a+2b+c$

$4a+2b+c=10$..........(2)

For n=3,

$M_3=a(3)^2+b(3)+c$

$18=9a+3b+c$

$9a+3b+c=18$..........(3)

(2)-(1) gives

$3a+b=6$..........(4)

(3)-(2) gives

$5a+b=8$..........(5)

(5)-(4) gives

$2a=2$

$\implies\boxed{\bf\,a=1}$

put a=1 in (4) we get

$3(1)+b=6$

$\implies\boxed{\bf\,b=3}$

Using the values of a and b in (1), we get

$1+3+c=4$

$\implies\boxed{\bf\,c=0}$

Answer 2

a=1

b=3

c=0

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