Question

Find the sum of all odd integers between 70 and 120​

Answer 1

It forms an AP

AP : 71 , 73 , 75 , .................. 119

a = 71

d = 2

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

119 = 71 + (n-1)2

n-1 = (119 - 71)/2

n = 24

`S_n` = n/2 × (a +
`a_n`)

= 24/2 × (71 + 119)

= 12 × 190 = 2280

Answer 2

To find the sum of all odd integers between 70 and 120, we calculate the number of odd integers in this range and use the sum of an arithmetic series formula. The sum is 2375, which is obtained using the formula (number of terms/2) × (first odd integer + last odd integer).

Step-by-step explanation:

The student's question pertains to finding the sum of all odd integers between 70 and 120. To solve this, we first identify the smallest odd integer greater than 70, which is 71, and the largest odd integer less than 120, which is 119.

We then use the formula for the sum of an arithmetic series, Sn = n/2 × (a1 + an), where n is the number of terms, a1 is the first term, and an is the last term.

To find n, we calculate the number of odd numbers from 71 to 119, which can be done by the formula (last term - first term)/2 + 1. In this case, n is (119 - 71)/2 + 1 = 25. So there are 25 odd integers between 70 and 120.

Substituting these values into the sum formula: S25 = 25/2 × (71 + 119) = 25/2 × 190 = 12.5 × 190 = 2375. Therefore, the sum of all odd integers between 70 and 120 is 2375.