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Arithmetic Progressions — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsArithmetic Progressions4 Marks
Question
While playing a treasure hunt game, some clues (numbers) are hidden in various spots collectively forms an A.P. lf the number on the $n^{th}$ spot is 20 + 4n, then answer the following questions to help the player in spotting the clues.
  1. Which number is on the first spot?.
  1. 20
  2. 24
  3. 16
  4. 28
  1. Which number is on the $(n - 2)^{th}$ spot?
  1. 16 + 4n
  2. 24 + 4n
  3. 12 + 4n
  4. 28 + 4n
  1. Which number is on the $34^{th}$​​​​​​​ spot?
  1. 156
  2. 116
  3. 120
  4. 160
  1. What is the sum of all the numbers on the first 10 spots?
  1. 410
  2. 420
  3. 480
  4. 410
  1. Which spot is numbered as 116?
  1. $5^{th}$
  2. $8^{th}$
  3. $9^{th}$
  4. $4^{th}$
✓

Answer

Number on $n^{th}$ spot $= 20 + 4n i.e., t_n = 20 + 4n$
  1. (b) 24
Solution:

Number on $1^{th}$ spot $= t_1 = 20 + 4(1) = 24​​​​​​​$​​​​​​​
  1. (c) 12 + 4n
Solution:

Number on $(n - 2)^{th}$ spot $= t_{n - 2}​​​​​​​$​​​​​​​

= 20 + 4 (n - 2)

= 20 + 4n - 8 = 12 + 4n
  1. (a) 156
Solution:

Number on $34^{th}$ spot $= t_{34}​​​​​​​$​​​​​​​

= 20 + 4(34) = 156
  1. (b) 420
Solution:

Here a $= t_1 = 24$ Now,$ t_2 = 20 + 4 (2) = 20 + 8 = 28$

$d = t_2 - t_1= 4$

So, required sum $=\text{S}_{10}=\frac{10}{2}\big[2(24)+9(4)\big]=420$
  1. (d) $4^{th}​​​​​​​$​​​​​​​
Solution:

Let $n^{th}​​​​​​​$​​​​​​​ spot is numbered as 116.

$\therefore$ $t_n = 11$

$\Rightarrow 20 + 4n = 116$

$\Rightarrow 4n = 96$

$\Rightarrow n = 24$

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