How to find the number of months required for progressive payment?

Question

Mathematics

Good evening!
I completely forgot the math
. We have a debt of 1'000'000
And we know that it needs to be repaid starting from 5,000 rubles and increases by 1 thousand every month.
How to calculate after what time we can repay the debt?
I decided that it is possible through an arithmetic progression, but I can’t deduce n from that formula ..

Answer 1

сумма = ( первый_месяц + последний_месяц ) * всего_месяцев / 2

for N months:
from here we
transform by
solving the equation we get
N \u003d -50 or +40
Answer 40

Answer 2

And what's so difficult about adding 1000 in a cycle and summing up the final payment by comparing it with the required one? The number of loop iterations will be the number of months