Question

Alka loves to organize cans in triangles piles, where each row has one can less than the

row below and there is only one can in the top row. To arrange 10 cans in total, she

places 4 cans in the bottom row and 3 cans in the row above it and so on:

i. Alka now arranges a pile having 20 cans in the bottom row, ending with one can in

the top row. The total number of cans in the arrangement are:__________________

ii. There are 820 cans in a pile. How many cans are there in the bottom now?

________________________

iii. Alka has 200 cans. Explain why she will not be able to organize the cans in a
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Answer 1

Answer:

1. 210

2. 40

3. value of n is irrational number so he cannot arrange.

Step-by-step explanation:

1. formula to calculate the total number of cans is n(n+1)/2.

Hans 20 (20 + 1) / 2 is equal to 210 option B .

2. number of cans in the bottom row =n

820=n(n+1)/2

n(n+1)/2=820gives n^2+n-1640=0

n=40 or -41;

n=-41 is rejected as n is a natural number.n=40

3. Alka will not be able to organise 200 cans in a triangular Pile.

let the total number of can be =S

a =1 and d =-1

number of rows be n

S= n/2 (2 + n-1)

200 = 1 / 2 (n+1)

400=n^2+n

n^2+n-400=0

the value of n is an irrational number

hence, he cannot make an arrangement using 200 cans.