Respuesta :
Answer:
The Sum Of The Integers From -6 To 58 is 1690.
Step-by-step explanation:
Given,
[tex]a=-6[/tex]
[tex]T_n=58[/tex]
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 [tex]a_1=-6\ and\ a_2=-5[/tex]
[tex]\therefore d=a_2-a_1=-5-(-6)=-5+6=1[/tex]
Now we use the formula of A.P.
[tex]T_n=a+(n-1)d[/tex]
On substituting the values, we get;
[tex]58=-6+(n-1)1\\\\n-1=58+6\\\\n-1=64\\\\n=64+1=65[/tex]
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.
[tex]S_n=\frac{n}{2}(2a-(n-1)d)[/tex]
On substituting the values, we get;
[tex]S_{65}=\frac{65}{2}(2\times-6+(65-1)1)\\\\S_{65}=\frac{65}{2}(-12+64)\\\\S_{65}=\frac{65}{2}\times52\\\\S_{65}=65\times26=1690[/tex]
Hence The Sum Of The Integers From -6 To 58 is 1690.
