The nth term of a sequence is 7n-4. Write down the 4th term and the 10th term of the sequence. The first four terms of a different sequence are 9, 13, 17, 21. Find an expression for the nth term of this sequence.

The nth term of a sequence means that when we substitute the value of n in to the equation, we find that term. So to find the 4th term in the sequence, we substitute 4 in for n. 7(4)-4=28-4=24. The 10th term is 7(10)-4=70-4=66.

Given a beginning of a sequence, we can find an expression for the nth term by first finding the difference between the values. The difference between 9 and 13 is 4, the difference between 17 and 13 is 4, and the difference between 21 and 17 is also 4. This tells us that the coefficient of n should be 4, because each time we move a position along, 4 is added. Then we need to find a starting value. The 1st term is 9, so we want to find a value x such that 4(1)+x=9. What is x? x must be 5 as 9-4=5. Therefore, an expression for the nth term of this sequence is 4n+5.

A good thing about these types of questions is that you can check your answer: using our expression, the 2nd term in the sequence should be 4(2)+5=8+5=13, which it is!