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✪

• He was on 21st step when all marbles are finished.

★EXPLAINATION★

☆GIVEN☆

• Total number of marbles = 441

• 1, 3, 5, .... marbles are placed on first, second, third steps and so on.

✯TO FIND✯

• Step Number when all marbles are finished.

᯽CONCEPT᯽

Sum upto nth term of an AP with first term 'a' and common difference 'd' is given by

$\boxed{\boxed{Sₙ = \frac{n}{2}[2a + (n-1)d]}}$

☆CALCULATION☆

Number of marbles placed on consecutives steps are 1, 3, 5, ........ They form an AP with

$\red{\boxed{a = 1, d = 3-1 = 2}}$

Since total number of marbles is 441

$Sₙ = 441$

$\frac{n}{2}[2a + (n-1)d]= 441$

$\frac{n}{2}[2\times 1 + (n-1)2]= 441$

$\frac{n}{2}[2n]= 411$

$n²= 411$

$n = 21$

Thus, he was on 21st step when all marbles are finished.

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