This question seems easy but I am struggling with it now, I tried a few ways and check this [solution][1] as well but couldn't help me, please check and help if you are able: 
So I need to save the sum of array elements in single variable and I tried these approaches, I show you two of them here. (**I must have x as variable to store result, and initialize the array as well**)

 Array [A, 3]
 A = {1, 2, 5}
 R2 = x == Sum[A[index], {index, i, 3}] && i == 1
 Simplify[Reduce[R2]]

And Also

 R2 = x == Sum[A[index], {index, i, 3}] && A[1] == 1 && A[2] == 2 && A[3] == 5 && i == 1
 Simplify[Reduce[R2]]

this is part of final answer I get

 x == A[1] + A[2] + A[3]

It shows me a simple equation not final answer, but I expect a simple answer **x== 8 or x-> 8**, but it does not solve the SUM, seems I am missing something. 

EDITED:
based on @thorimur answer I completed my question. 
Actually the reason i used Reduce and Sum is:
1- I used reduce because we have more complicated expressions which Sum is part of that. 
2- I used sum because not all the time we have initialized array. For some times, i need parametric array which must be shown in Sum. this is the more complete statement. 

 


 R2 = x == Sum[A[index], {index, i, 3}] && i == 1
 R3=Simplify[Reduce[
 Exists[{i,x,A}, R2 && // Array initialization // i == 1 ]]]

I know this does not work but this is my intention. we need a statement as R3 
 


 [1]: https://mathematica.stackexchange.com/questions/23677/how-to-sum-over-a-list