(n+1)2-1
15(1)
35 * * * * * That is the next term. The question, however, is about the nth term. And that is 6*n - 1
It is 6n+5 and so the next term will be 35
If you layout the sequence... 3, 8, 15, 24, 35... ok so you find the difference between these 3 to 8= +5 8 to 15= +7 15 yo 24= +9 24 to 35= +11 so now you find something called the second difference which is +2 +2 +2 +2 +2. Then you need to divide the second difference by 2 which is just n^2 as it is a quadratic sequence you are finding. now you do the nth term which is just 1 2 3 4 5 etc. and you do your n squared sequence which is 1 4 9 16 25 etc. and you do your sequence 3 8 15 24 35 you find out that you need from the n squared sequence and your regular sequence which is +2 +4 +6 +8 +10 this is your 2n add 2n to the divided term n squared and you have your answer, Answer= n squared +2n ------> (n^2)+2n
It is: nth term = 35-9n
(n+1)2-1
15(1)
35 * * * * * That is the next term. The question, however, is about the nth term. And that is 6*n - 1
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.
It is 6n+5 and so the next term will be 35
The given sequence (7, 14, 21, 28, 35,....) is an arithmetic sequence where each term increases by 7. The nth term of the given sequence is 7n
If you layout the sequence... 3, 8, 15, 24, 35... ok so you find the difference between these 3 to 8= +5 8 to 15= +7 15 yo 24= +9 24 to 35= +11 so now you find something called the second difference which is +2 +2 +2 +2 +2. Then you need to divide the second difference by 2 which is just n^2 as it is a quadratic sequence you are finding. now you do the nth term which is just 1 2 3 4 5 etc. and you do your n squared sequence which is 1 4 9 16 25 etc. and you do your sequence 3 8 15 24 35 you find out that you need from the n squared sequence and your regular sequence which is +2 +4 +6 +8 +10 this is your 2n add 2n to the divided term n squared and you have your answer, Answer= n squared +2n ------> (n^2)+2n
Divide the sequence by 5 and the answer becomes very obvious: 1, 4, 9, 16,...N2 So, 5, 20, 45, 80,...5N2
This is an arithmetic progression. In general, If an A.P. has a first term 'a', and a common difference 'd' then the nth term is a + (n - 1)d. In the sequence shown in the question, the first term is 0 and the common difference is 5, therefore the nth term is, 0 + (n - 1)5. This can be rearranged to read : 5(n - 1) For example : the 7th term is 30 : 5(7 - 1) = 5 x 6 = 30.
t(n) = n2 + 5n - 1
If the nth term is n*7 then the first 5 terms are 7, 14, 21, 28, 35.