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[Maximum mark: 6]

Consider an arithmetic sequence $2,6,10,14,\dots$

1. Find the common difference, $d$. [2]
   

2. Find the $10$th term in the sequence. [2]
   

3. Find the sum of the first $10$ terms in the sequence. [2]
   

[Maximum mark: 6]

The table shows the first four terms of three sequences: $u_n$, $v_n$, and $w_n$.

1. State which sequence is

   1. arithmetic;

   2. geometric. [2]
      

2. Find the sum of the first $50$ terms of the arithmetic sequence. [2]
   

3. Find the exact value of the $13$th term of the geometric sequence. [2]
   

[Maximum mark: 7]

1. Write down the quadratic expression $3x^2 + 5x - 2$ in the form $(ax-b)(x+c)$.[2]
   

2. Hence, or otherwise, find the coefficient of the term in $x^9$ in the expansion
   of $(3x^2+5x-2)^5$. [5]