Originally Posted by

**GrigOrig99** Hi, first time poster.

**Q.** In the sequence u1, u2, u3,…,un,

u1 = 0, u2 = 3, u3 = 12 and un = a + bn + cn^2

Find the values of a, b and c.

**Attempt: **

If n = 1 then u1 = a + b(1) + c(1)2 = 0

= a + b + c = 0

If n = 2 then u2 = a + b(2) + c(2)2 = 3

= a + 2b + 4c = 3

If n = 3 then u3 = a + b(3) + c(3)2 = 12

= a + 3b + 9c = 12

= a + b + c = 0

= a + 2b + 4c = 3

= a + 3b + 9c = 12

It's been a number of years since I've last studied maths. Can anyone help me on what comes next? Many thanks.