Find the next two terms of an arithmetic sequence wherein k-1, 13, and 3k+3 are consecutive terms.

Question:

Find the next two terms of an arithmetic sequence wherein k-1, 13, and 3k+3 are consecutive terms.

Arithmetic Sequences

An arithmetic sequence is a set of terms where the difference between any two consecutive terms is a constant. The difference between the terms is known as the common difference. For example, the following set of terms consisting of the set of odd counting numbers is a simple arithmetic sequence:

{1, 3, 5, 7, ..., {eq}2n-1 {/eq}, ...}

with a common difference of 2 and the general term being given by {eq}2n-1 {/eq}. When the terms in an arithmetic sequence are added together, we have an arithmetic series.

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We are given the following consecutive terms in an arithmetic sequence:

$$k-1,\ 13,\ 3k+3$$

The common difference is given by:

\begin{align} 1...