Question

Is there any formula to find: sum of numbers between 1 to 100? If so, plz state a d do so

Answer 1

Yes !!

Formula for finding the Sum of the numbers between 1 to 100 = n/2 × [ 2a + ( n - 1 ) × D ] Where n = Number of terms ; a = First term ; D = Common difference.

Solution : AP = 1 , 2 , 3 , ......... 100.

Here,

First term ( a ) = 1

Common difference ( D ) = Second term - First term = 2 - 1 = 1.

And,

Last term ( Tn ) = 100

a + ( n - 1 ) × d = 100

1 + ( n - 1 ) × 1 = 100

1 + n - 1 = 100

n = 100

Number of terms ( n ) = 100

Therefore,

Sum of the numbers between 1 to 100 = N/2 × [ 2A + ( n - 1 ) × D

=> 100/2 × [ 2 × 1 + ( 100 - 1 ) × 1 ]

=> 50 × ( 2 + 99 )

=> 50 × 101

=> 5050.

Second formula :

Sn = N/2 × [ First term + Last term ]

Here,

N = 100

So,

S100 = 100/2 × ( 1 + 100 )

=> 50 × 101

=> 5050

Answer 2

Wel Yes. There is...

I will Give its Derivation. Now.

By using The Equation of A.P. To Find the sum of n terms....
i.e.

Sn =(n/2)[2a+(n-1)×d]


Here.
1 is the First term.

and The common Difference is also 1.
by substututing this...

→Sn=(n/2[2(1)+(n-1)(1)]
→Sn=(n/2)[(2+n-1)]
→Sn=(n/2)[n+1]

→Sn=n(n+1) /2

But If you need The sum of 100 terms..
100×101/2=10100/2=5050 is the answer...

Hope it Helps..
Regards,...