Differences of Squares of Triangular Numbers and Converse

Q. Write cubes of 4 natural numbers which are of the form 3n + 1 (e.g.

4, 7, 10, .........) and verify the following: 'The cube of a natural

number of the form 3n + 1 is a natural number of the same form'. [4 MARKS]

Q. If the product of two numbers is 21 and their difference is 4, then the ratio of the sum of their cubes to the difference of their cubes is:

1. 185 : 165
2. 165 : 158
3. 185 : 158
4. 158 : 145

Q.

(a) What kind of numbers do you get if you add consecutive triangular numbers? Give examples.
(b) $\angle E$ is a complement of $\angle F$ and $\angle E$= ${28}^{\circ }$. Find $\angle F$.
[2 MARKS]

Q. $\begin{array}{ccc}6& 9& 135\\ 5& 7& 76\\ 8& 11& ....\end{array}$