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A city based NGO is organising a competition to break 'Dahi Handi' by forming a human pyramid on the occasion of Janmashtami. One troop with 400 members decided to participate in the competition. They planned to build eleven level pyramid with level one being at the bottom and level eleven being at the top. Level one has 41 members, level two has 37 members, level three has 33 members and so on.
Based on the above information, answer the following questions :
(i) What is the number of members at level eleven? (1 Mark)
(ii) Find the number of members at the third level from the top. (1 Mark)
(iii) (a) Find the total number of members who formed the human pyramid. (2 Marks)
OR
(iii) (b) At which level is the number of members 5 times the number of members at level ten? (2 Marks)
Based on the above information, answer the following questions :
(i) What is the number of members at level eleven? (1 Mark)
(ii) Find the number of members at the third level from the top. (1 Mark)
(iii) (a) Find the total number of members who formed the human pyramid. (2 Marks)
OR
(iii) (b) At which level is the number of members 5 times the number of members at level ten? (2 Marks)
Show SolutionHide Solution↓
(i) The number of members at the level eleven $= a_{11}$
$= 1$ (1 Mark)
(ii) The number of members at the third level from the top $= a_9$
$= 9$ (1 Mark)
(iii) (a) The total number of members who formed the human pyramid
$S_{11} = \frac{11}{2} [41+1]$ (1/2 Mark)
$= 231$ (1/2 Mark)
OR
(iii) (b) Let $n^{th}$ level be the required level
$a_n = 5 a_{10}$ (1 Mark)
$41 + (n - 1) (-4) = 5 [41 + 9(-4)]$ (1/2 Mark)
$(n - 1) (-4) = -16$
$n = 5$ (1/2 Mark)
At $5^{th}$ level the number of members is 5 times the number of members at level ten
$= 1$ (1 Mark)
(ii) The number of members at the third level from the top $= a_9$
$= 9$ (1 Mark)
(iii) (a) The total number of members who formed the human pyramid
$S_{11} = \frac{11}{2} [41+1]$ (1/2 Mark)
$= 231$ (1/2 Mark)
OR
(iii) (b) Let $n^{th}$ level be the required level
$a_n = 5 a_{10}$ (1 Mark)
$41 + (n - 1) (-4) = 5 [41 + 9(-4)]$ (1/2 Mark)
$(n - 1) (-4) = -16$
$n = 5$ (1/2 Mark)
At $5^{th}$ level the number of members is 5 times the number of members at level ten