Question

the sum 3+5+9+....n=___

Answer 1

The sum of first n odd numbers (1+3+5+7...n) is n ²

But here 1 is not given in equation of odd numbers....

Sum is....n ²-1

This also satisfies the A.P.

Hppe this helps you....

Answer 2

Ans.

The common difference (d) = 2
The first element (a) = 3.

So, the n-th term is
I = a + (n-1).d
= 3 + (n-1)×2
= 1 + 2n.

So the required sum is
= (n/2)(a + I)
= (n/2)( 3 + 1 + 2n)
= (n/2)(4 + 2n)
= n (n+2)


OR,
The sum of first nth terms of odd numbers is
n^2.
But 1 is missing.

So the sum be (n^2 - 1).