How we can combine two different series and add them

Suppose we have two different sets of arithmetic series ranging from 1 to n. how to combine or add them together so that the elements are not repeated.

[KSSV]

Is output a series or a number ?

[phoenix]

output should be the total expression for n numbers

[KSSV]

That's what...it would be a number...adding numbers is not a deal...

[Cong Ba]

Could you provide an input&output pair so people understand what you expect?

Answer 1

[John BG]

1.

generating 2 sequences

p=randi([-10 10],1,12)
q=randi([-10 10],1,12)

p =
     7     9    -8     9     3    -8    -5     1    10    10    -7    10

q =
    10     0     6    -8    -2     9     6    10     3   -10     7     9

2.

calculating X

either by applying the first expression directly

p([1:2:end]).*q([2:2:end])
 =
     0    64    27   -50  -100   -63

X=sum(p([1:2:end]).*q([2:2:end]))
=
  -122

or adding q(0)=0 just in case

q=[0 q]
X=sum(p([1:2:end]).*q([2:2:end]))
=
  -122

same result

3.

calculating Y

Y=sum(p([2:2:end]).*q([1:2:end]))

   =
     266

if you find this answer useful would you please be so kind to consider marking my answer as Accepted Answer?

To any other reader, if you find this answer useful please consider clicking on the thumbs-up vote link

thanks in advance

John BG

<mailto:[e-mail] [e-mail]>

Answer 2

[Jan]

If you provide the input data and show what you have tried so far, posting an answer would require less guessing. I guess that p and q are vectors with n = length(p) / 2. Then what about:

X = 0;
for k = 2:2:n+1
  X = X + p(k) * q(k-1);
end

Y = 0;
for c = 2:n
  Y = p(2 * c) * q(2 * c - 1);
end

R = X + Y;

Note that I've shifted the indices by one, because they start at 1 in Matlab, not at 0, such that q(k-1) would fail for k=1. If this replies the wanted result, try:

R = sum(p(2:2:n+1) .* q(1:2:n)) + sum(p(2 * (2:n)) .* q(2 * (2:n) - 1))

or slightly faster:

R = sum(p(2:2:n+1) .* q(1:2:n)) + sum(p(4:2:2*n) .* q(4:2:2*n-1))