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![{\displaystyle \ a_{1},a_{2},...a_{n}....\qquad in\ cui\quad a_{n}-a_{n-1}=d\ (costante),}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6566096602ba47f461062e45d559f45b93245e9b)
![{\displaystyle \ a_{n}=a_{1}+(n-1)d,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/975bf6adaef9f993d58e2e6a18de1e4468f5147c)
am= termine centrale=
media aritmetica,
![{\displaystyle \ S_{n}={a_{1}+a_{n} \over 2}\ n;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/548d38cdc7fb712270106a9f8f2aa35d13d79bd6)
- Sn (somma primi n numeri interi) =
![{\displaystyle {\frac {n(n+1)}{2}},}](https://wikimedia.org/api/rest_v1/media/math/render/svg/95ddac71a0633d095918a7c88e118cc0cdcf238e)
- S2n (somma primi n numeri pari) =
![{\displaystyle \ n(n+1),}](https://wikimedia.org/api/rest_v1/media/math/render/svg/126d809f0fee9e9b6f7aab0df9fcfbca5f38d312)
- S2n+1 (somma primi n numeri dispari) = n2.
![{\displaystyle \ a_{1},a_{2},....a_{n}....}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f2279c171800b58eed393f59609f7cfbeaf634af)
![{\displaystyle {a_{n+1} \over a_{n}}=q\ (costante),}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6d139f850fa29457cf768440d3effd337397e523)
termine centrale
media geometrica,
![{\displaystyle \lim _{n\to \infty }S_{n}=a_{1}{1-q^{n} \over 1-q},\qquad se\quad |q|<1,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/eb0e893ccde03b6682a0707592e8cd0e4beeda5e)
![{\displaystyle \ P_{n}^{2}=(a_{1}a_{n})^{n},\qquad P_{n}={\sqrt {(a_{1}a_{n})^{n}}}.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ed70ef9b2a6df04be6924990953722c0b97d99c0)
I numeri a, m, b formano una progressione armonica se i loro inversi:
formano una progressione aritmetica;
- la media armonica fra
e
è:
![{\displaystyle \ m={2ab \over a+b}.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ffe336a06c591735e189521c1932e87aa4d4d795)