Evaluate enter only the sum

Question

S₂₈for -143+(-134)+(-125)+(-116)+........

Answer 1

The formula for the first n terms of an arithmetic sequence, starting with n = 1, is:
∑a_n = [a₁ + (n - 1)d], where d is the difference between the terms

The sum is, in effect, n times the "average" of the first and last terms. This sum of the first n terms is called "the n-th partial sum".

 

The difference between the terms given in this question is +9; a₁ = -143, and n = 28

 

So, our equation becomes ∑a₂₈ = (-143 + (28 -1 )9)

 

Which becomes -143 + (27)9 = -143 +243 = +100

 

 

Answer 2

first, write the function that describes the terms ("i" = the number of the term)

 

We see that the value is -143, increased by 9 on each successive term, so the reduction is 9 (i -1)  (On the first term, there is no increase)

 

So...

f (i ) = -143 + (i - 1)(9)

Test it

f(1) = -143

f(2) = -134

etc........

 

Now expand the equation and simplify:

f (i) = 9i - 152

 

Now, write the summation ∑, for i=1 to 28, of i:...... 28 (28+1)/2 = 406

 

finally, we can write 9 (406 ) - 28 (152) = -602

 

Look at the basic rules here:

https://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/summationdirectory/Summation.html