Case Study Question 05

Mathematics

Chapter 5: Arithmetic Progressions

Class 10

Birthdays are important for each one of us. Smriti is celebrating her birthday. She invited her friends for a party. She arranged a number card game. In this game, number cards are distributed among her friends such that they are following an Arithmetic progression.
Smriti made sure that each of her friends who stood in a row gets a card. The first three cards marked `2x`, `x+10` and `3x+2` is given to Rahul, Sonu and Sanjay respectively.
Based on the above information answer the questions:

Question.1.
Sonu is a curious child. She wants to find the sum of the number cards obtained by her, Rahul, and Sanjay. From the above given information, help her to do so.

To find the sum of the number on the cards,first find `x`.
As the terms are in AP,
`(x+10)-2x =(3x+2)-(x+10)`
⇒ `x = 6`
∴ Sum of the number cards of Rahul, Sonu and Sanjay is `2x +x+10 + 3x+2=6x +12 = 48`

Question.2.
Smriti has called only a few of her close friends as the Covid pandemic is spreading. Ratan is her friend who gets the last card with the number 56. If so, find how many of Smriti’s friends are attending the birthday party.

To find the number card ,find the first term (a) and common difference (d)
`a = 12` and `d = 4`
Let Ratan occupy the `n^{th}` position.
`\Rightarrow a_{n} = a + (n – 1) d`
`\Rightarrow 56 = 12 +(n-1)4`
`\Rightarrow n = 12`.
Hence, Smriti’s 12 friends attended the party.

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