Question

i had 441 marbels i went on arrangeing them like this one marble on first step, three on second,five on third.....so on .on which step i was when all marbels were finished

Answer 1

Answer:-

Given:

There are 441 marbles.

And,

These are arranged like 1 marble on 1st step , 3 marbles on 2nd step, 5 marbles on 3rd step....

If we assume that, these marbles are arranged in an Arithmetic sequence, the number of steps are taken as number of terms and the number of marbles are their values.

That means,

1 , 3 , 5 .... are in AP.

Hence,

• a (first term) = 1

• d (common difference) = 3 - 1 = 2.

And,

Total number of marbles = sum of n terms.

→ S(n) = 441

Now we have to find the value of n (the step on which maximum number of marbles (till 441) are arranged)

We know that,

Sum of first n terms of an AP = n/2 * [2a + (n - 1)d]

→ 441 = n/2* [2a + (n - 1)d]

→ 441 = n/2 * [2(1) + (n - 1)(2)]

→ 441 = n/2 * [2 + 2n - 2]

→ 441 = n/2 * (2n)

→ n² = 441

→ n² = (21)²

→ n = 21

Hence, the total number of marbles are being arranged till the 21st step.