Review question

Ref: R9507

## Suggestion

1. Write down the next three members of the sequence of numbers$1,4,9,16,\dotsc$
2. Calculate the 300th member of the sequence.

Is this sequence familiar?

1. Calculate the first five members of the sequence of differences$4-1\ ,9-4\ ,16-9,\dotsc$
2. If $a$,$b$,$c$, are consecutive members of the sequence in (i) write down a formula connecting $c-b$ and $b-a$. Rewrite this formula so $b$ is the subject.

What is this sequence of differences? Can we find a pattern connecting three consecutive numbers?

1. Use the result of (iv) and the fact that $8677^2 = 75290329 \qquad \text{ and} \qquad 8679^2 = 75325041$ to calculate $8678^2$ making your method clear.

Can we use our result from earlier in the problem?