To find the nth term of the sequence 5, 15, 29, 47, 69, we first determine the differences between consecutive terms: 10, 14, 18, and 22. The second differences are constant at 4, indicating that the nth term is a quadratic function. By fitting the quadratic formula ( an^2 + bn + c ) to the sequence, we find that the nth term is ( 2n^2 + 3n ). Thus, the nth term of the sequence is ( 2n^2 + 3n ).
By varying the parameters of a quartic polynomial, the nth term can be made whatever you like. But, taking the simplest solution, Un = 2 - 4n for
They are: nth term = 6n-4 and the 14th term is 80
14+9n
t(n) = (-5n4 + 62n3 - 247n2 + 334n - 36)/6
It is: nth term = -4n+14
This is an arithmetic sequence which starts at 14, a = 14, and with a common difference of -1, d = -1. We can use the nth term formula an = a + (n - 1)d to get an = 14 + (n - 1)(-1) = 14 - n + 1 = 15 - n.
The given sequence is decreasing by 2 each time, starting from 12. To find the nth term, we can use the formula for an arithmetic sequence: (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. In this case, (a_1 = 12), (d = -2), and we need to find the general formula for the nth term. Therefore, the nth term for the sequence 12 10 8 6 4 is (a_n = 12 + (n-1)(-2)), which simplifies to (a_n = 14 - 2n).
Oh, dude, you're hitting me with the math questions, huh? So, the formula for finding the nth term of an arithmetic sequence is a + (n-1)d, where a is the first term and d is the common difference. In this sequence, the common difference is 8 (because each term increases by 8), and the first term is 14. So, the formula for the nth term would be 14 + 8(n-1). You're welcome.
25
1,7,13,19
The given sequence appears to be increasing by 10 each time. To find the nth term, we can use the formula for arithmetic sequences: nth term = first term + (n-1) * common difference. In this case, the first term is 4 and the common difference is 10. Therefore, the nth term for this sequence would be 4 + (n-1) * 10, which simplifies to 10n - 6.
Tn = 10 + n2
Well, isn't that just a lovely pattern we have here? Each term is increasing by 4, isn't that delightful? So, if we want to find the nth term, we can use the formula: nth term = first term + (n-1) * common difference. Just like painting a happy little tree, we can plug in the values and find the nth term with ease.
The differnace between the numbr is 7, therefore the first part of the formula will be 7n, now for the first term we replace n with one so nx7=7 and to get to 10 you need to add 3 making the nth term 7n+3, To check your answer you must replace n with the two (for the second term) which comes to 14 to get to seventeen you need to add three so the formula nth term 7n+3, hope this helped
f(n) = 14 - 6n -6n+20
To find the nth term of the sequence 5, 15, 29, 47, 69, we first determine the differences between consecutive terms: 10, 14, 18, and 22. The second differences are constant at 4, indicating that the nth term is a quadratic function. By fitting the quadratic formula ( an^2 + bn + c ) to the sequence, we find that the nth term is ( 2n^2 + 3n ). Thus, the nth term of the sequence is ( 2n^2 + 3n ).