Quadratic sequences

Question 1

How can the nth term of a quadratic sequence be written?

Answer 1

u[n] = an[2] + bn + c

Question 2

How do you find the nth term of a quadratic sequence?

Answer 2

u[n] = an[2] + bn + c

1) the second difference/2 is ‘a’
2) write out the sequence an[2]
3) take it away from the original sequence
4) the first difference in the new sequence becomes ‘b’
5) write out an[2] + bn
6) take the new sequence away from the old one
7) the one value you are left with becomes ‘c’

Question 3

When working out quadratic sequences, which way around do you always subtract the sequences, and which sequence is always the same?

Answer 3

original - new

the original sequence is always the one taken away from

Question 4

The first terms of a quadratic sequence are 5, 9, 17, 29, 45…

Work out the nth term of this sequence.

Answer 4

2n[2] - 2n + 5

Question 5

A quadratic sequence is 1, 3, 6, 10, 15…

Work out an expression for the nth term.

Answer 5

1, 3, 6, 10, 15
+2, +3, +4, +5
+1, +1, +1

1/2 = 0.5n[2]

0.5n[2] =
0.5, 2, 4.5, 8, 12.5 - (1, 3, 6, 10, 15) =
0.5, 1, 1.5, 2, 2.5
+0.5

0.5n[2] + 0.5n =
1, 3, 6, 10, 15 - (1, 3, 6, 10, 15) = 0, 0, 0, 0, 0
0.5n[2] + 0.5n + 0

0.5n[2] + 0.5n