Progressions

N-th member of arithmetical progression
$$a_{n} = a_1+d\cdot (n-1)$$
a1 - first member
d - common difference of an arithmetical progression
n - member number
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      =   
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Members of of an arithmetical progression and arithmetic average
$$a_{n} = \frac{a_{M1}+a_{P1}}{2}$$
a_n - n-th member
a_M1 - (n-1)-th member
a_P1 - (n+1)-th member
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      =   
Calculate 'a_n'

Sum of the members of an arithmetic progression (arithmetic series)
$$S_{n} = \frac{(2\cdot a_{1}+d\cdot (n-1))\cdot n}{2}$$
a1 - first member
d - common difference of an arithmetical progression
n - member number
Find   It is known that:
      =   
Calculate 'S_n'

Sum of the members of an arithmetic progression (arithmetic series)
$$S_{n} = \frac{(a_{1}+a_{n})\cdot n}{2}$$
a1 - first member
a_n - n-th member
n - member number
Find   It is known that:
      =   
Calculate 'S_n'

N-th member of geometric progression
$$b_{n} = b_1\cdot q^{(n-1)}$$
b1 - first member
q - common ratio of a geometric progression
n - member number
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      =   
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Members of geometric progression and geometric average
$$b_{n} = \sqrt {b_{M1}\cdot b_{P1}}$$
b_n - n-th member
b_M1 - (n-1)-th member
b_P1 - (n+1)-th member
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      =   
Calculate 'b_n'

Sum of the members of geometric progression (geometric series)
$$S_{n} = \frac{b_1\cdot (q^{n}-1)}{q-1}$$
b1 - first member
q - common ratio of a geometric progression
n - member number
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      =   
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Sum of the members of geometric progression (geometric series)
$$S_{n} = \frac{b_{n}\cdot q-b_1}{q-1}$$
b1 - first member
b_n - n-th member
n - member number
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      =   
Calculate 'S_n'

Sum of an infinite geometric progression (infinite geometric series)
$$S_{n} = \frac{b_1}{1-q}$$
b1 - first member
q - common ratio of a geometric progression
Find   It is known that:
      =   
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