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?