To find the nth term of the sequence -2, -8, -18, -32, -50, we first observe the differences between consecutive terms: -6, -10, -14, -18. The second differences (which are constant at -4) suggest that the nth term can be represented by a quadratic function. The general form is ( a_n = An^2 + Bn + C ). Solving for coefficients A, B, and C using the first few terms gives the nth term as ( a_n = -2n^2 + n ).
37
The given sequence is a geometric sequence where each term is multiplied by 2 to get the next term. The first term (a) is 4, and the common ratio (r) is 2. The nth term of a geometric sequence can be found using the formula ( a_n = a \cdot r^{(n-1)} ). Therefore, the nth term of this sequence is ( 4 \cdot 2^{(n-1)} ).
To find the nth term of this sequence, we first need to identify the pattern. The differences between consecutive terms are 5, 9, 13, 17, and so on. These are increasing by 4 each time. This means that the nth term can be calculated using the formula n^2 + 4n + 1. So, the nth term for the sequence 5, 10, 19, 32, 49 is n^2 + 4n + 1.
7n - 3
The nth term is 7n-3 and so the next term will be 39
The nth term is (36 - 4n)
the sequence is Un=2n2
The nth term is 2n2. (One way to find that is to notice at all the numbers are even, then divide them by 2. The sequence becomes 1, 4, 9, 16, 25, which are the square numbers in order.)
The given sequence is an arithmetic sequence with a common difference of 7 (18-11=7, 25-18=7, and so on). To find the nth term of 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 position of the term, and d is the common difference. In this case, the first term a_1 is 11 and the common difference d is 7. So, the nth term of this sequence is 11 + (n-1)7, which simplifies to 11 + 7n - 7, or 7n + 4.
37
The given sequence is a geometric sequence where each term is multiplied by 2 to get the next term. The first term (a) is 4, and the common ratio (r) is 2. The nth term of a geometric sequence can be found using the formula ( a_n = a \cdot r^{(n-1)} ). Therefore, the nth term of this sequence is ( 4 \cdot 2^{(n-1)} ).
The nth term in the sequence means an unspecified number an unspecified distance along the series. 8 16 32 64 128... n. It is also a shothand notation so the reader knows that the sequence continues.
To find the nth term of this sequence, we first need to identify the pattern. The differences between consecutive terms are 5, 9, 13, 17, and so on. These are increasing by 4 each time. This means that the nth term can be calculated using the formula n^2 + 4n + 1. So, the nth term for the sequence 5, 10, 19, 32, 49 is n^2 + 4n + 1.
If the nth term is 8 -2n then the 1st four terms are 6, 4, 2, 0 and -32 is the 20th term number
7n - 3
The nth term is 2n2. (One way to find that is to notice at all the numbers are even, then divide them by 2. The sequence becomes 1, 4, 9, 16, 25, which are the square numbers in order.)
The nth term is 7n-3 and so the next term will be 39