We are looking for a pattern in the given sequence. Let's have a look at the difference between consecutive terms in the first five elements of the sequence.
A sequence is arithmetic if it can be written in the following form.
t(n)=t(1)+m(n-1)
In this form m is the common difference. For an arithmetic sequence, the common difference is constant. However, as we saw from Part A, this is not true for the given sequence. Therefore, it cannot be an arithmetic sequence. However, it is still possible to calculate the sum of the series.
We must divide the sequence in two separate sequences. As we can see, the sequence can be thought of as two different sequences, both with a common difference of 5, but one starts from 5 and the other starts from 3.
c
As explained in Part B, we can think of the original sequence as two separate sequences.
t(n):& 5+10+15+...+395+400
a(n):& 3+8+13+...+393+398
Therefore, if we calculate the sum of each sequence and add the results we can determine the sum of the original sequence. Let's first write their equations.
t(n)=5+5(n-1)
a(n)=3+5(n-1)
To calculate the sum of each series we need to know how many elements they contain. Notice that they will contain exactly the same number of elements, so we only need to determine this for one of them. By setting t(n) equal to 400 we can solve for n.
