Find the sum of the first $13$ terms of the arithmetic progression $4, 7, 10, 13, \dots$

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Solve $x^{2} - x - 12 = 0$ and give the larger root.
Solve the simultaneous equations $2 x + 3 y = 38$ and $x - 4 y = - 25$ . Find the value of $x + y$ .
If $y = 4 x^{2} - 6$ , find $x$ when $y = 58$ and $x > 0$ .
Find the sum of the first $16$ terms of the arithmetic progression $6, 8, 10, 12, \dots$
The length of a rectangle is $2 cm$ more than its width. Its area is $15 cm^{2}$ . Find the width.
In an arithmetic progression the term number $3$ is $6$ and the term number $6$ is $18$ . Find the term number $25$ .