Treasure Hunt is an exciting and adventurous game where participants follow a series of clues/numbers/maps to discover hidden treasures. Players engage in a thrilling quest, solving puzzles and riddle

Question

Treasure Hunt is an exciting and adventurous game where participants follow a series of clues/numbers/maps to discover hidden treasures. Players engage in a thrilling quest, solving puzzles and riddles to unveil the location of the coveted prize.

While playing a treasure hunt game, some clues (numbers) are hidden in various spots collectively forming an A.P. If the number on the $n^{	ext{th}}$ spot is $20 + 4n$, then answer the following questions to help the players in spotting the clues:

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(i) Which number is on first spot?
(ii) (a) Which spot is numbered as $112$?

**OR**

(ii) (b) What is the sum of all the numbers on the first $10$ spots?
(iii) Which number is on the $(n - 2)^{	ext{th}}$ spot?

Accepted Answer

Step 1: (i) Number on first spot $= 20 + 4 	imes 1 = 24$
Step 2: (ii)(a) $20 + 4n = 112 \Rightarrow 4n = 92 \Rightarrow n = 23$
Step 3: (iii) Number on $(n - 2)^{	ext{th}}$ spot $= 20 + 4(n - 2) = 12 + 4n$

Question

Solution