Replace me by the sum of my cyclic successors!
MATL, 10 9 bytes

"G@:X@+)s


Try it online!

&#9;% implicit input
"&#9;% for loop, iterate over the input array&#32;
G&#9;% push input x
@&#9;% push for loop index, x[i]
:&#9;% range, push [1,...,x[i]]
X@&#9;% push for loop index, i
+&#9;% sum, so stack holds [i+1,...,i+x[i]]
)&#9;% index, modularly, so gets the cyclic successors
s&#9;% sum cyclic successors, leaving the sum on the stack
&#9;% implicit end of for loop
&#9;% implicit output of stack