Please help me **Consider the following recursively defined sequence.**\( t_k = t_{k-1} + 3k + 1, \) for each integer \( k \geq 1 \) \( t_0 = 0 \)The steps below begin an iterative process to guess an explicit formula for the sequence.\[\begin{align*}t_0 & = 0 \\t_1 & = t_0 + 3 \cdot 1 + 1 = 3 + 1 \\t_2 & = t_1 + 3 \cdot 2 + 1 = (3 + 1) + 3 \cdot 2 + 1 = 3 + 3 \cdot 2 + 2 \\t_3 & = t_2 + 3 \cdot 3 + 1 = (3 + 3 \cdot 2 + 2) + 3 \cdot 3 + 1 = 3 + 3 \cdot 2 + 2 + 3 \cdot 3 + 3\end{align*}\]Continue the iteration process in a free response. Then guess a formula for \( t_n \) as a summation written in expanded form, and use Theorem 5.2.1 to write it as a single fraction whose denominator is 2. (Submit a file with a maximum size of 1 MB.)**File Upload:**[Choose File] No file chosen*Note: This answer has not been graded yet.*

Name: Please help me **Consider the following recursively defined sequence.*
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Please help me **Consider the following recursively defined sequence.**\( t_k = t_{k-1} + 3k + 1, \) for each integer \( k \geq 1 \) \( t_0 = 0 \)The steps below begin an iterative process to guess an explicit formula for the sequence.\[\begin{align