Any number that you choose can be the nth number. There are infinitely many rules, based on a polynomial of order 5, such that the first five numbers are as listed in the question. There are also non-polynomial solutions. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one.
Using the principle of Occam's razor, the answer is
U(n) = 10*n
6n+10
n(n+1)
3 x 10(n-1)
The difference between the terms increases by 2 each time. 20-12=8 30-20=10 42-30=12 56-42=14 ... f(n)=(n+2)(n+3)
35
Say if you had the pattern 15 20 25 30 35 40 45 50 To find the nth term you have to see what the gap between the numbers is. In our case this is 5. Then you have to find out what the difference between the gap and the first number. In this sequence it is 10. So your answer would be..... 5n+10 That's how you find the nth term.
6n+10
n(n+1)
The given sequence is an arithmetic sequence with a common difference of 5. To find the nth term of an arithmetic sequence, we 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. In this case, the first term (a_1 = 0) and the common difference (d = 5). Therefore, the nth term of the sequence is (a_n = 0 + (n-1)5 = 5n - 5).
3 x 10(n-1)
The difference between the terms increases by 2 each time. 20-12=8 30-20=10 42-30=12 56-42=14 ... f(n)=(n+2)(n+3)
35
Clearly here the nth term isn't n25.
90
here t1=2 t2=6 t3=12 t4=20 t5=30 the nth term is n(n+1) for t1 = 1(1+1)=2 for t2=2(2+1)=6 for t3=3(3+1)=12 for t4=4(4+1)=20 for t5=5(5+1)=30 for tn=n(n+1)
Well, honey, if the nth term is 3n-1, then all you gotta do is plug in n=30 and do the math. So, the 30th term would be 3(30)-1, which equals 89. There you have it, sweet cheeks, the 30th term of that sequence is 89.
You can see that all the numbers go up by 7. This means that the first part of the nth term rule for this sequence is 7n. Now, you have to find out how to get from 7 to 3, 14 to 10, 21 to 17 ... this is because we are going up in the 7 times table. To get from the seventh times table to the sequence, you take away four. So the answer is : 7n-4