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W- wirl T- tighten
The expression ( T(n) = 6n - 1 ) represents a sequence where ( n ) is the term number. To find the first term, substitute ( n = 1 ): ( T(1) = 6(1) - 1 = 6 - 1 = 5 ). Thus, the first term is 5.
To find any term of a geometric sequence from another one you need the common ration between terms: t{n} = t{n-1} × r = t{1} × r^(n-1) where t{1} is the first term and n is the required term. It depends what was given in the geometric sequence ABOVE which you have not provided us. I suspect that along with the 10th term, some other term (t{k}) was given; in this case the common difference can be found: t{10} = 1536 = t{1} × r^9 t{k} = t{1} × r^(k-2) → t{10} ÷ t{k} = (t{1} × r^9) ÷ (t{1} × r^(k-1)) → t{10} ÷ t{k} = r^(10-k) → r = (t{10} ÷ t{k})^(1/(10-k)) Plugging in the values of t{10} (=1536), t{k} and {k} (the other given term (t{k}) and its term number (k) will give you the common ratio, from which you can then calculate the 11th term: t{11} = t(1) × r^9 = t{10} × r
It is T/2 * (t+1)
If the first term, t(1) = a and the common difference is r then t(n) = a + (n-1)*r where n = 1, 2, 3, ...
It is a version of the Fibonacci sequence, where each term is the sum of the previous two terms. The sequence is defined by the recursive formula: t(n) = t(n-1) + t(n-2) where t(n) is the nth term Here, t(1) = 2 and t(2) = 3 though for the more general form of the Fibonacci sequence, t(1) = 1 and t(2) = 1.
t(1) = 1 t(2) = 1 t(n+1) = t(n) + t(n-1) for n = 1, 2, 3, ... That is, the first two terms are 1; after that every term is the sum of the previous two terms.
It refers to the fact that when lain flat a T-shirt resembles a letter T.The "T" was never meant to stand for anything - the etymology is based on the shape of a T-shirt when it's laid flat, and how the body and sleeves make a capital-T shape. The term has its origins around 1920.
Suppose A is the first term and R is common difference. Then, if t(n) is the nth term, t(n) = A + n*R Then t(5) = A + 5R and t(3) = A + 3R so that t(5) - t(3) = 2R Now t(1) = A + R = A + 3R - 2R (since R = 3R - 2R) So t(1) = t(3) - 2R You were given t(3) and have calculated 2R above, so can work out t(1).
t(n) = t(n - 1) + (10n - 9)
Too Smart To Stand For This Garbage
1 For Sorrow Two For Joy (Magpie Song)