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Case Study - 2
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 $n^{th}$ spot is $20+4n$, then answer the following questions to help the players in spotting the clues :
(i) Which number is on first spot?
(ii) (a) Which spot is numbered as $112$?
OR
(b) What is the sum of all the numbers on the first $10$ spots?
(iii) Which number is on the $(n - 2)^{th}$ spot ?
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 $n^{th}$ spot is $20+4n$, then answer the following questions to help the players in spotting the clues :
(i) Which number is on first spot?
(ii) (a) Which spot is numbered as $112$?
OR
(b) What is the sum of all the numbers on the first $10$ spots?
(iii) Which number is on the $(n - 2)^{th}$ spot ?
Show SolutionHide Solution↓
(i) Number on the first spot $$\begin{aligned}& = 20 + 4 \times 1 = 24 \\ & \text{(ii) (a) } 20 + 4n = 112 \\ & \Rightarrow n = 23 \\ & \text{OR} \\ & \text{(ii) (b) } d = 4 \\ & S_{10} = \frac{10}{2} [2 \times 24 + 9 \times 4] \\ & = 420 \\ & \text{(iii) Number on the } (n - 2)^{th} \text{ spot } = 20 + 4(n - 2) \\ & = 12 + 4n\end{aligned}$$