Math, asked by kadukavita79, 1 year ago

The sum of 3+5+7+9+....n=____

Answers

Answered by Swarup1998

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)

Swarup1998: why u are thinking in that way... take it as a series of elements with difference 2.

Swarup1998: first term as 3... common difference as 2.

Swarup1998: so n-th term is {3 + 2 (n-1)}

Swarup1998: i.e., 2 + 2n.

Swarup1998: so the sum of the AP is

Swarup1998: (n/2)( 1st term + n-th term)

kadukavita79: hmmm....but my teacher told this way

kadukavita79: are you a college student...???

Swarup1998: i am a college student

Swarup1998: this answer is also right... u can satisfy the sum too... put n=1,2,...

Answered by Anonymous

$\huge\bf\fbox\red{Answer:-}$

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).

Previous Question

Next Question