## How to find the cumulative sum of numbers in a list by adding a constant value?

As you specifically mentioned numpy:

`import numpy as np`

initial_value = 5

constant_value = 3

desired_list_size = 7

result = np.arange(desired_list_size) * constant_value + initial_value

This starts with a range from 0 to 7 (exclusive) then it multiplies each element by 3 and in the end it adds 5 to each element.

Note: the result size is actually equal to `desired_list_size`

and not one larger as in your question.

## Loop through list elements to get cumulative sums

You're not far from the answer. You just need to begin your range from the next num in the list. Try this:

`data = [5, 4, 3, 2, 1]`

for ind, num in enumerate(data):

perf = [sum(data[ind:i+1]) for i in range(ind, len(data))]

print(perf)

Output:

`[5, 9, 12, 14, 15]`

[4, 7, 9, 10]

[3, 5, 6]

[2, 3]

[1]

## Python Running Sum in List

If you'd like a numpy solution

`from numpy import cumsum`

result = list(cumsum(a))

## Modified cumulative sum of numbers in a list

This should solve your problem:

`def changelist (l, t):`

subset = sum(l) / t

current, total = 0, 0

for x in l:

total += x

if total > subset:

current, total = current + 1, x

yield current

Examples:

`>>> list(changelist([1, 4, 5], 2))`

[0, 0, 1]

>>> list(changelist([1, 2, 3, 4, 2, 5, 1, 6], 4))

[0, 0, 0, 1, 1, 2, 2, 3]

>>> list(changelist([1, 2, 3, 4, 2, 5, 1, 6], 2))

[0, 0, 0, 0, 0, 1, 1, 1]

How does it work?

`current`

stores the "id" of the current subset,`total`

the sum of the current subset.- For each element
`x`

in your initial list`l`

, you add its value to the current`total`

, if this`total`

is greater than the expected sum of each subset (`subset`

in my code), then you know that you are in the next subset (`current = current + 1`

) and you "reset" the total of the current subset to the actuel element (`total = x`

).

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