The first four terms of an arithmetic sequence are : 11, 17, 23, 29. In terms of n, find an expression for the nth term of this sequence.

An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. We can work this out for the sequence 11, 17, 23, 29. To go from the 1st term (11) to the 2nd term (17), we have to add 6. Therefore, the difference between consecutive terms is 6. This means if we knew the value of the 1st term, and we wanted to calculate the value of the 3rd term, we would have to perform the following calculation: 11 + (26) = 23. This is equal to what we have seen in the sequence! Similarly, if we wanted to calculate the value of the 4th term, we would have to perform 11 + (36) = 29. To get from the first term to any term in the sequence (let's call this the 'nth term'), we have to add 6 multiplied by (n-1). We multiply by (n-1) because that is the number of times we have to add 6, to get to the nth term. So, we can state an expression for the nth term of the sequence as: value of nth term = 11 + (n-1)*6. Extension: How can this formula be generalised for an arithmetic sequence if the value of the 1st term was equal to a, and the difference between consecutive terms equal to d