n(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)
Looks like 57: 12+9=21, +9=30, +9=39, +9=48, +9=57.
6n+10
When n=30, 3n-1 = 89 .
n(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)
> 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
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.
Clearly here the nth term isn't n25.
90
Looks like 57: 12+9=21, +9=30, +9=39, +9=48, +9=57.
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).
6n+10
When n=30, 3n-1 = 89 .
The nth term is 7n-5 and so the 6th term will be 37
Just plug in 30 for n in 3n-1. The answer is 89.