Question

Question: Find The Sum Of The Integers From -6 To 58 Of Ss. O 1,500 O 1,734 O 1,690 O 1,621​

Answer 1

The Sum Of The Integers From -6 To 58 is 1690.

Explanation:

Given,

`a=-6`

`T_n=58`

We have to find out the sum of integers from -6 To 58.

Firstly we will find out the total number of terms that is 'n'.

Here
`a_1=-6\ and\ a_2=-5`

`\therefore d=a_2-a_1=-5-(-6)=-5+6=1`

Now we use the formula of A.P.

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

On substituting the values, we get;

`58=-6+(n-1)1\\\\n-1=58+6\\\\n-1=64\\\\n=64+1=65`

So there are 65 terms in between -6 To 58.

That means we have to find the sum of 65 terms in between -6 To 58.

Now we use the formula of Sum of n_terms.

`S_n=(n)/(2)(2a-(n-1)d)`

On substituting the values, we get;

`S_(65)=(65)/(2)(2*-6+(65-1)1)\\\\S_(65)=(65)/(2)(-12+64)\\\\S_(65)=(65)/(2)*52\\\\S_(65)=65*26=1690`

Hence The Sum Of The Integers From -6 To 58 is 1690.