10.4 The nth term of a quadratic sequence — Practise

1. Find the nth term of $2,6,12,20,30,\ldots$.

Answer: $n^2+n$.

2. Find the nth term of $3,10,21,36,55,\ldots$.

Answer: $2n^2+n$.

3. Find the nth term of $4,11,22,37,56,\ldots$.

Answer: $2n^2+n+1$.

4. Continue $1,5,13,25,41,\ldots$ by one term.

Answer: $61$.

5. Find the 10th term of $n^2+3n$.

Answer: $130$.

6. Does $n^2+2n+2$ generate $4,8,14,22$?

Answer: No: at position 1 it gives 5, not 4.

7. The first differences are $5,9,13,17$. Find the constant second d

Answer: $4$.

8. H The nth term is $n^2+4n$. Find $n$ when the term is 45.

Answer: $n=5$.