The sequence $c_1 + c_4 + c_7 + c_{10} + \dots$ represents the sum of terms from a larger sequence $c_n$, where each term is selected at intervals of 3 (i.e., the sequence skips two terms between each consecutive term).

To solve this, let's break down the process:

Step-by-Step Solution:

1. Define the General Term of the Sequence:
   If we have a sequence $\{ c_n \}$, the general term at position $n$ is represented as $c_n$.

2. Identify the Pattern:
   In this sequence, we start from $c_1$ and increment by 3 for each subsequent term, giving us the terms: $c_1, c_4, c_7, c_{10}, \dots$ This implies that each term in our new sequence can be written in terms of the original sequence $c_n$ as: $c_{3k - 2}$ where $k$ is the position in the new sequence (starting from $k = 1$).

3. Express the Sum of Terms in the New Sequence:
   Now that we have established the terms in the sequence are of the form $c_{3k - 2}$, the sum of the first $m$ terms in this sequence is: $S_m = c_1 + c_4 + c_7 + \dots + c_{3m - 2}$

4. Evaluating the Sum (if a formula for $c_n$ is given):
   To evaluate the sum $S_m$, we need to know the general formula for $c_n$. For instance, if $c_n$ follows an arithmetic or geometric sequence, we can apply corresponding sum formulas.

Would you like help evaluating this sum for a specific formula for $c_n$ or is this a general inquiry?

Questions to Expand on:

1. What is the specific formula or pattern of $c_n$ in this sequence?
2. Is there a particular number of terms $m$ you need for the sum?
3. Would you like to consider the sum of an infinite series if it applies?
4. Are there any constraints or initial conditions for the sequence $c_n$?
5. Would you like a formula to generalize the sum for any given sequence pattern?

Tip: For arithmetic or geometric progressions, knowing the first term and the common difference or ratio can greatly simplify finding the sum of sequences.