If we want to find the nth term of this sequence, the first thing we need to do is work out the progression (in other words, how the sequence progresses from one term to the next). We simply write the progression as a number, then put “n” after it.
We know that this sequence increases by 5 each time, so the first thing we do is write 5n.
All we then need to do is consider the sequence we would generate with the expression we have just written. Think of it this way: 5n means the 5 times table; 6n means the 6 times table; and so on.
In our example of 5n, the sequence would be 3,8,13,18, … We just have to compare this to the sequence we have
an = a1 + (n-1)d
a9 = 3 + (9 - 1) 5
a9 = 3 + (8)5
a9 = 3 +40
a9 = 43
So, finding the nth term is really as simple as seeing how much the sequence changes by, then comparing it to the relevant times table. Let us now look at how we can use this to work out any given term. If you have an expression for the nth term and want any given term number, you just have to substitute your term number for “n”.
Answers & Comments
Answer:
If we want to find the nth term of this sequence, the first thing we need to do is work out the progression (in other words, how the sequence progresses from one term to the next). We simply write the progression as a number, then put “n” after it.
We know that this sequence increases by 5 each time, so the first thing we do is write 5n.
All we then need to do is consider the sequence we would generate with the expression we have just written. Think of it this way: 5n means the 5 times table; 6n means the 6 times table; and so on.
In our example of 5n, the sequence would be 3,8,13,18, … We just have to compare this to the sequence we have
an = a1 + (n-1)d
a9 = 3 + (9 - 1) 5
a9 = 3 + (8)5
a9 = 3 +40
a9 = 43
So, finding the nth term is really as simple as seeing how much the sequence changes by, then comparing it to the relevant times table. Let us now look at how we can use this to work out any given term. If you have an expression for the nth term and want any given term number, you just have to substitute your term number for “n”.
#CarryOnLearning