Sequencing is actually a topic that falls under number and place value however when we want to find the NTH term we now actually branch into algebra
Algebra is also used with sequencing, each number in a sequence is called a term and the value of any term in a sequence can be worked out by using the rule for that sequence for example 2, 4, 6, 8, 10 … the three dots symbolise that the sequence continues using this rule. When we look at this sequence, we can see that the rule for each term equals the previous term +2. Knowing this we are able to create a method to find what we call the NTH term. The value for a particular term can be found out without writing out the entire sequence up to that point by writing the rule as an expression we can use the expression to work out the term for the above example the expression would be 2n. So, this is the process we would follow:
2N means 2 x 1 = 2 here the one shows we are looking for the first term of the sequence.
If we wanted to find the second term in a sequence, we would replace the end with 2, creating the equation 2 x 2 = 4 . If we wanted to find the 41st term 41 would replace n, making an equation 2 x 41 = 82, for the thousandth term we would times 2 by 1000 giving us 2000.
Another example could be 2, 6, 10, 14, 18… Now with this sequence we could write the expression in two ways 4n – 2. Now this sounds a little complicated, but the reason is written like this is because we must always multiply by the place in the sequence. For example, 4n – 2 is 4 x 1 – 2 = 2, if we wanted to find the fifth term, we would say 4 times 5 – 2 gives us 18.
Now let’s break this down further, when we are trying to find the NTH term of a sequence, we must remember to find the nearest multiple for each number in the sequence. Technically we do not need to plus or minus anything, but we must multiply by something even if it is one. As we saw in our first example all the numbers in the sequence were a part of the two times tables that meant we didn’t need to plus or minus anything in the rule however in our second example all the numbers were close enough to the multiples within the four times table, but we then need to subtract 2 to follow the rules specifically.