8. Case study question

Question:

4 m.

In a video game, a player begins with $16$ coins. After each level, the number of coins becomes $three$ times the previous number, and then $2$ extra coins are awarded.

ChatGPT Image Jul 29, 2026, 07_33_59 PM.png

(i) Which of the following sequences represents the first five terms of this scenario?

$2, 53, 1376, 4133, 458, 12392$
$2, 53, 458, 155, 1379$
$2, 53, 4133, 155, 12392$
$16, 50, 152, 458, 1376$

(ii) Find its General term

$a_{n} = 2 a_{n - 1} + 16, n \geq 2$
$a_{n} = 3 a_{n - 1} + 2$
$a_{n} = 3 a_{n - 1} + 2, n \geq 2$
$a_{n} = 3 a_{n - 1}, n \geq 2$

(iii) Find its next two terms

$4133, 12392$
$4130, 12392$
$155, 458$
$458, 53$

(iv) Which of the following is a recursive rule for the sequence?

$a_{n} = 16 n - 5.9$
$a_{n} = 5.9 a_{n - 1} + 2$
$a_{n} = 16 (n - 1) - n^{2}$
$a_{n} = 16 n + 17$

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