Mathematics, 23.10.2020 20:10, 20guadalupee73248

Consider the following recursively defined sequence. $t_{k} = t_{k-1} + 3k + 1$ , for each integer k ≥ 1
The steps below begin an iterative process to guess an explicit formula for the sequence.
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.

$t_{0} = 0$
$t_{0} = 0$
$t_{1} = t_{0} + 3 * 1 + 1 = 3 + 1\\t_{2} = t_{1} + 3 * 2 + 1 = (3 + 1) + 3 * 2 + 1 = 3 + 3 * 2 + 2\\t_{3} = t_{2} + 3 * 3 + 1 = (3 + 3 * 2 + 2) + 3 * 3 + 1 = 3 + 3 * 2 + 3 * 3 + 3$

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Consider the following recursively defined sequence. , for each integer k ≥ 1

The steps...