# Summation of all odd numbers from 1 to 451

13 views (last 30 days)
Zacharia on 19 Aug 2022
Commented: Voss on 19 Aug 2022
The following lines accurately sum when d (common difference) is 1, however, as soon as it changes, I get a wrong answer, does anyone understand why? I assume I am quite ignorant, but I would love any help I can get:
% Initialize n, a, d and s
n = 451;
a = 1;
d = 2;
S = 0;
% Compute S by adding the terms
for i = 1:n
S = S+a+(i-1)*d;
end
%Call S
S
Command Window:
S = 203401
• Where S should actually equal: 51,076

VBBV on 19 Aug 2022
Edited: VBBV on 19 Aug 2022
n = 451;
a = 1;
d = 2;
S = 0;
% Compute S by adding the terms
for i = 1:n
S(i) = (a+(i-1)*d/2);
end
sum(S(1:2:end)) % sum of all odd numbers
ans = 51076
Zacharia on 19 Aug 2022
Thankyou so much, I understand more from both answers now!
I truly appreciate your help, have a lovely day :)

Voss on 19 Aug 2022
The for loop iterates n times, so after it's done, S represents the sum of n terms, which is fine when d = 1, but when d > 1, the summation you want has less than n terms.
In other words, there are 451 integers between 1 and 451 (inclusive), but only (451+1)/2 = 226 odd integers in that range and only (451+2)/3 = 151 integers congruent to 1 mod 3 (i.e., 1, 4, 7, 10, ...) in that range.
So "for i = 1:n" must be modified to take into account the value of d, so that the loop iterates the correct number of times.
Zacharia on 19 Aug 2022
That perfectly explains why it only worked for d = 1, I see now.
Thankyou so much for taking time out of you day to explain it, truly helped me
Voss on 19 Aug 2022
You're welcome!

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