



 
Hi Zoe, If you look at the terms in your sequence you will see that the terms all decrease by 3 each time. This constant difference makes your sequence an arithmetic sequence. There is a formula for finding the nth term of an arithmetic sequence: t_{n} = a + (n1)d where tn represents the nth term In your sequence, a = 5, and d = 3. Since we are looking for an expression for the nth term, we leave n as n and we get that:
If you wanted to expand and simplify this expression just distribute the 3 through the brackets and combine the constants:
You can verify that this formula does in fact produce the terms you already know: Your first term (when n=1) t_{1} = 8  3(1) = 5 And now that you have the formula, you could find the value of any term, you'd just need to know what n value you wanted. Suppose you wanted to find the 84th term. All you'd have to do is substitute 84 for n and evaluate the righthand side:
Hope this helps,  


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