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angicarl
The answer would be 3n^2 + 2.

This can be found/proven by replacing "n" with term number (1,2,3,4...), then solving to get the final number. For example 3 * 1^2 + 2. You would first do 1^2, which is 1. Next, you would multiply 1 by 3, to get 3. Finally, you'd and the 2 to get 5. 5 is the 1st term, and you can use this same equation to get the rest of the terms you need.

I hope this helps!
xero099

The expression for the nth term for the Sequence is [tex]S(n) = 5 + \Sigma^{n}_{i= 1} [9 +6\cdot (n-1)][/tex].

This Sequence is an example of an Arithmetic Sum, as Difference between two consecutive Terms in increasing monotonously, whose definition is described below:

[tex]S(n) = a_{o} +\Sigma^{n}_{i = 1} r(n)[/tex] (1)

Where:

  • [tex]n[/tex] - Index of the element
  • [tex]r(n)[/tex] - Rate function.

Where the Rate Function for this Sequence has the following form:

[tex]r(n) = 9 + 6\cdot (n-1)[/tex] (2)

The expression for the nth term for the Sequence is: ([tex]a_{o} = 5[/tex])

[tex]S(n) = 5 + \Sigma^{n}_{i= 1} [9 +6\cdot (n-1)][/tex]

The expression for the nth term for the Sequence is [tex]S(n) = 5 + \Sigma^{n}_{i= 1} [9 +6\cdot (n-1)][/tex].

Please see this question related to Sums: https://brainly.com/question/5117026

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