It is: -3072
It is: -3072
A geometric sequence is a sequence where each term is a constant multiple of the preceding term. This constant multiplying factor is called the common ratio and may have any real value. If the common ratio is greater than 0 but less than 1 then this produces a descending geometric sequence. EXAMPLE : Consider the sequence : 12, 6, 3, 1.5, 0.75, 0.375,...... Each term is half the preceding term. The common ratio is therefore ½ The sequence can be written 12, 12(½), 12(½)2, 12(½)3, 12(½)4, 12(½)5,.....
This is a geometric series with common ratio 2. The nth term is un = -3*2(n-1) So u11 = -3*2(11-1) = -3*210 = -3*1024 = -3072
To find the value of the nth term in an arithmetic sequence, you can use the formula: (a_n = a_1 + (n-1)d), where (a_n) is the nth term, (a_1) is the first term, (n) is the term number, and (d) is the common difference between terms. In this sequence, the first term (a_1 = 12) and the common difference (d = -6 - 0 = -6). So, the formula becomes (a_n = 12 + (n-1)(-6)). Simplifying this gives (a_n = 12 - 6n + 6). Therefore, the value of the nth term in this arithmetic sequence is (a_n = 18 - 6n).
12 - 5(n-1)
> since the value rises by nine at each step and the first term is 12 the formula for > the nth term is: 12+(n-1)*9 Which simplifies to Sn = 9n + 3
To find the nth term of a sequence, we first need to identify the pattern or rule governing the sequence. In this case, the sequence appears to be increasing by 4, then 8, then 12, then 16, and so on. This pattern suggests that the nth term can be represented by the formula n^2 + n, where n is the position of the term in the sequence. So, the nth term for the given sequence is n^2 + n.
t(n) = 12*n + 5
12
An arithmetic sequence is a series of numbers in which each term is obtained by adding a constant value, called the common difference, to the previous term. In contrast, a geometric sequence is formed by multiplying the previous term by a constant value, known as the common ratio. For example, in the arithmetic sequence 2, 5, 8, 11, the common difference is 3, while in the geometric sequence 3, 6, 12, 24, the common ratio is 2. Thus, the primary difference lies in how each term is generated: through addition for arithmetic and multiplication for geometric sequences.
Yes, that's what a geometric sequence is about.
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