lex3340
23.03.2020 •
Mathematics
Can someone explain what geometric sequences are?
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Ответ:
Explanation:
A sequence is a list of numbers.
A geometric sequence is a list of numbers such that the ratio of each number to the one before it is the same. The common ratio can be any non-zero value.
Examples
1, 2, 4, 8, ... common ratio is 227, 9, 3, 1, ... common ratio is 1/36, -24, 96, -384, ... common ratio is -4___
General Term
Terms of a sequence are numbered starting with 1. We sometimes use the symbol a(n) or an to refer to the n-th term. The general term of a geometric sequence, a(n), can be described by the formula ...
a(n) = a(1)×r^(n-1) . . . . . n-th term of a geometric sequence
where a(1) is the first term, and r is the common ratio. The above example sequences have the formulas ...
a(n) = 2^(n -1)a(n) = 27×(1/3)^(n -1)a(n) = 6×(-4)^(n -1)You can see that these formulas are exponential in nature.
__
Sum of Terms
Another useful formula for geometric sequences is the formula for the sum of n terms.
S(n) = a(1)×(r^n -1)/(r -1) . . . . . sum of n terms of a geometric sequence
When |r| < 1, the sum converges as n approaches infinity. The infinite sum is ...
S = a(1)/(1-r)
Ответ:
4 x 6 = 24
3 x 6 = 18
7 x 6 = 42
Then add 24 +18 +42 which would equal to 84
So the expression you would write for this problem is
P (7)
Hope this helped!