Question

sum of all odd numbers from 1 to 200​

Answer 1

Answer:

odd number are 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29 ,191,193,195,197,200

Answer 2

Answer:

The sum of all the odd numbers from 1 to 200​ is 9950.

Step-by-step explanation:

By using the AP we can find the sum of all odd numbers from 1 to 100.

Formula by AP for finding the number of odd numbers present in 1 to200-

              $T_{n} =a + (n-1)d$ --------------------(i)

where,

• Number of terms is n
• Initial number is a = 1
• Difference between number is d = 2
• The last number is  $T_{n}$ = 199.

Now, from equation (i) and put the values in it-

               $T_{n} =a + (n-1)d$

                199 = 1 + (n-1)2

               199 - 1 = (n-1)2

               $\dfrac{198}{2} = n-1$

                99 + 1 = n

                n = 100  terms

Now, formula for the sum in AP-

                 $S_{n} =\dfrac{n}{2}(1+(n-1)\times2)$

                 $S_{100} =\dfrac{100}{2}(1+(100-1)\times2)$

                 $S_{n}$ = 50(1 + 198)

                 $S_{n}$ = 50×199

                 $S_{n}$ = 9950