# The first three terms of a sequence are a, b, c. The term-to-term rule of the sequence is 'Multiply by 2 and subtract 4'. Show that c = 4(a – 3).

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As the answer is given in the question, it's really important that you lay out your working carefully to give a convincing account as to how you got from the question to the answer.

Here we have a sequence. This means that there is a fixed rule that determines how you get from one number to the next... or here, from one letter to the next, because the question is using an algebraic progression.

The first letter in our sequence is a. To get to b we must multiply by 2 and subtract 4. a multiplied by 2 is 2a, and then subtracting 4 gives 2a - 4. Therefore, b = 2a-4.

To get to the third letter in our sequence, c, we must take b and again multiply by 2 and subtract 4. As b = 2a-4, we must multiply this by 2, giving 2(2a-4) and then subtract 4, giving 2(2a-4) - 4. It is very important here to consider the brackets. Remember that we are doubling b, and so we must double the entire expression that we now have for b, and so we put brackets around it.

So now we have c = 2(2a-4) - 4. This isn't quite the expression that we are working towards, but we can get there by expanding and then re-factorising. To expand the bracket, we multiply everything inside it by 2. This gives 4a - 8. Subtracting the other 4 gives c = 4a - 12. We can now go straight to the answer in the question, because both terms of the expression (4a and -12) are divisible by 4, giving c = 4((4a/4) - (12/4)) = 4(a-3).

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