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Formulas of arithmetical and geometrical progressions
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Arithmetic progression:
Progression's elements:
a
_{1}
,
a
_{2}
,
a
_{3}
, ... ,
a
_{n}
Progression's denominator:
d
Progression's element calculation formulas:
a
_{i+1}
=
a
_{i}
+
d
a
_{i}
= ½
(
a
_{i − 1}
+
a
_{i + 1}
)
Progression's n-th element calculation formulas:
a
_{n}
=
a
_{1}
+
(
n
−
1
)
d
Sum of the first n-elements of progression formulas:
S
_{n}
= ½
n
(
a
_{1}
+
a
_{n}
)
S
_{n}
= ½
n
(
2
a
_{1}
+
(
n
−
1
)
d
)
Geometric progression:
Progression's elements:
b
_{1}
,
b
_{2}
,
b
_{3}
, ... ,
b
_{n}
Progression's denominator:
q
, if |
q
| <
1
, then progression is called infinitely decreasing progression
Progression's element calculation formulas:
b
_{i+1}
=
b
_{i}
q
b
_{i}
^{2}
=
b
_{i − 1}
b
_{i + 1}
Progression's n-th element calculation formulas:
b
_{n}
=
b
_{1}
q
^{ (n − 1)}
Sum of the first n-elements of progression formulas:
Sum of the infinitely decreasing progression's formula
Useful links:
Logarithms identities