9 ,16 ,23, 30
We note that there is a difference of '7' between terms.
So the first part of the 'nth' term is 7n.
Note the '7' becomes multiple.
Next we need to find the constant 'c'
So taking the first term (n = 1) we write.
7n + c = 9
7(1) + c = 9
7 + c = 9
c = 2
So the 'nth' term is '7n + 2'
To verify , try the 3rd term n= 3 then answer should be '23'.
7(3) + 2 =
21 + 2 = 23 As required.
The nth term is 7n-5 and so the 6th term will be 37
35 * * * * * That is the next term. The question, however, is about the nth term. And that is 6*n - 1
It is T(n) = n2 + 4*n + 2.
If you meant: 2 12 22 32 then the nth term = 10n-8
A simple answer, based on a linear rule is U(n) = 5n - 23 for n = 1, 2, 3, ...
The rule for the nth term is t(0) = 23 t(n) = mod[t(n-1) + 2n-1, 26] for n = 1, 2, 3, ...
If you're asking what the nineth erm is, it's 58. The pattern is to add 7 to a umber to get the next number. 2+7=9, 9+7=16, 16+7=23, and so on.
Yes, the explicit rule for a geometric sequence can be defined from a recursive formula. If the first term is 23 and the common ratio is ( r ), the explicit formula can be expressed as ( a_n = 23 \cdot r^{(n-1)} ), where ( a_n ) is the nth term of the sequence. This formula allows you to calculate any term in the sequence directly without referencing the previous term.
14+9n
2n +29
Assuming the pattern would continue: 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13...
The 'n'th term is [ 13 + 5n ].