Loading

Let us look at an example first, imagine there is the following sequence:2, 4, 6, 8, 9, 10...Let the difference be constant d, in this case d = 2If I were to ask what would be the value of the 10th number in the sequence, how would you calculate it?a_{1}= 2a_{2 }= 4so if you just keep on adding a_{10} = 18This is easy if the numbers are small, however what if I were to ask for the 100th number or even 10000th number?To make it easier we need to come up with a formula that can calculate it let's substitute the numbers with variables. Let's take the previous example.a_{1}= 2 ;a_{2 }= 4 ; a_{2 }- a_{1}= 2 = d ;if we rearrange this equation,a_{2}= a_{1} + d ;a_{3}= a_{2} + d = a_{1} + d + d ;a_{4}= a_{3} + d = a_{1} + d + d +d ;

do you see a trend, its always one added d a_{n} = a_{1} + (n-1)*dSo let us say I would want to know what given that d = 2 and the initial value a_{1} = 2 and I want to find the 20th value, if we use the equationa_{n} = a_{1} + (n-1)*da_{20} = 2 + (20 -1)*2 = 2 +19*2 = 2 + 38 = 40

One to one online tution can be a great way to brush up on your Maths knowledge.

Have a Free Meeting with one of our hand picked tutors from the UK’s top universities

Find a tutor

One to one online tution can be a great way to brush up on your Maths knowledge.

Have a Free Meeting with one of our hand picked tutors from the UK’s top universities

Find a tutor