Find the sum of the first 20 terms of the arithmetic progression $3, 7, 11, 15, \dots$

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In an arithmetic progression, the 4th term is 14 and the 9th term is 29. What is the first term $a_{1}$ ?
In a geometric progression with all positive terms, the second term is 6 and the fifth term is 48. What is the common ratio $r$ ?
Determine the infinite sum of the convergent geometric series: $9 + 3 + 1 + \frac{1}{3} + \dots$
A sequence satisfies the recurrence relation $a_{n + 1} = 2 a_{n} + 3$ with $a_{1} = 1$ . What is the general formula for $a_{n}$ ?
Evaluate the summation: $\sum_{k = 1}^{10} (3 k^{2} - 2 k)$ .