n'th term:
n^2 + 5
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The sequence given is an arithmetic sequence, where each term is obtained by adding a fixed difference to the previous term. The difference between consecutive terms is increasing by 3 each time (3, 5, 7, 9). To find the nth term of this sequence, we can use the formula for the nth term of 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 position of the term, and (d) is the common difference. In this case, the first term is 6 and the common difference is increasing by 3 each time. So, the nth term for this sequence is (6 + (n-1)3), which simplifies to (3n + 3).
Oh, isn't that just a beautiful sequence of numbers? To find the pattern, we can see that each number is increasing by adding consecutive odd numbers: 3, 5, 7, 9. So, to find the nth term, we can use the formula n^2 + 5.
Well, well, well, aren't we feeling fancy with our arithmetic sequence? The pattern here is that each number is increasing by adding consecutive odd numbers (1, 3, 5, 7, etc.). So, the nth term formula for this sequence is n^2 + 5. Keep calm and carry on with your math wizardry!
n squared + 5
> 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
90
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.
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