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UPSKILL MATH PLUS

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Subjects
Mathematics CBSE
Class 9 New
Predicting What Comes Next: Exploring Sequences and Progressions
Case Based Questions

1. Case study question

Exercise condition:

4 m.

In a video game, a player begins with $18$ coins. After each level, the number of coins becomes $three$ times the previous number, and then $5$ 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?

$5, 59, 1658, 4979, 551, 14942$
$18, 59, 182, 551, 1658$
$5, 59, 4979, 182, 14942$
$5, 59, 551, 182, 1658$

(ii) Find its General term

$a_{n} = 3 a_{n - 1}, n \geq 2$
$a_{n} = 3 a_{n - 1} + 5$
$a_{n} = 5 a_{n - 1} + 18, n \geq 2$
$a_{n} = 3 a_{n - 1} + 5, n \geq 2$

(iii) Find its next two terms

$4979, 14942$
$182, 551$
$4979, 14942$
$551, 59$

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

$a_{n} = 18 (n - 1) - n^{5}$
$a_{n} = 18 n - 5.5$
$a_{n} = 18 {(n - 1)}^{2} + 5.5$
$a_{n} = 5.5 a_{n - 1}$

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