Question

The sum of consecutive odd numbers 1+3+5+.........+k is 1000000 find k

Answer 1

The correct answer is 1999999

because,
$\frac{1999999 + 1}{2} = \frac{2000000}{2} = 1000000$

Answer 2

Answer:

The value of k is 1999.

Step-by-step explanation:

The given series is

1+3+5+.........+k

It is an AP. Here, first term is 1 and common difference is 2.

The sum of n terms of an AP is

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

The sum of n terms is 1000000.

$1000000=\frac{n}{2}[2(1)+(n-1)2]$

$1000000=n(1+n-1)$

$1000000=n^2$

$1000=n$

Total number of terms in the series is 1000.

The nth term of an AP is

$a_n=a+(n-1)d$

$a_{1000}=1+(1000-1)2$

$k=1999$

Therefore the value of k is 1999.