- (a) Calculate the sum of all the even numbers from 2 to 100 inclusive,
$$2 + 4 + 6 + \ldots \ldots + 100$$
(b) In the arithmetic series
$$k + 2 k + 3 k + \ldots \ldots + 100$$
\(k\) is a positive integer and \(k\) is a factor of 100 .
- Find, in terms of \(k\), an expression for the number of terms in this series.
- Show that the sum of this series is
$$50 + \frac { 5000 } { k }$$
(c) Find, in terms of \(k\), the 50th term of the arithmetic sequence
$$( 2 k + 1 ) , ( 4 k + 4 ) , ( 6 k + 7 ) , \ldots \ldots ,$$
giving your answer in its simplest form.