The given problem is written in Gujarati and can be translated as follows:

Problem: A sequence has the general term $a_n = 5 - 6n$. Find the sum of the first $n$ terms of this sequence.

This is a problem involving an arithmetic progression (AP), where the $n$-th term $a_n$ is provided. Let's go through the steps to solve it.

Steps:

1. Identify the first term and common difference: The formula for the $n$-th term of an arithmetic progression (AP) is: $a_n = a_1 + (n - 1) d$ But in this case, the $n$-th term is directly given by $a_n = 5 - 6n$.

   • For $n = 1$, $a_1 = 5 - 6(1) = 5 - 6 = -1$.
   • For $n = 2$, $a_2 = 5 - 6(2) = 5 - 12 = -7$.
   • The common difference $d$ is the difference between consecutive terms, i.e., $d = a_2 - a_1 = -7 - (-1) = -6$.

   So, the first term $a_1 = -1$, and the common difference $d = -6$.

2. Sum of the first $n$ terms of an AP: The sum of the first $n$ terms of an arithmetic progression is given by: $S_n = \frac{n}{2} \times (2a_1 + (n - 1)d)$ Substituting the values: $S_n = \frac{n}{2} \times \left( 2(-1) + (n - 1)(-6) \right)$ Simplifying the expression: $S_n = \frac{n}{2} \times \left( -2 - 6(n - 1) \right)$ $S_n = \frac{n}{2} \times (-2 - 6n + 6)$ $S_n = \frac{n}{2} \times (4 - 6n)$ $S_n = n \times \frac{4 - 6n}{2}$ $S_n = n \times (2 - 3n)$ So, the sum of the first $n$ terms is: $S_n = n(2 - 3n)$

This gives the sum of the first $n$ terms of the arithmetic progression as $S_n = n(2 - 3n)$.

Would you like a more detailed breakdown of this solution? Here are some related questions you can consider:

1. How do you derive the sum formula for an arithmetic progression?
2. What is the significance of the common difference in an arithmetic progression?
3. How can you verify the result using specific values of $n$?
4. What is the sum of the first 5 terms using the formula $S_n = n(2 - 3n)$?
5. How does this sequence behave as $n$ increases?

Tip: For sequences, identifying patterns like common differences or ratios is crucial to solving sum-related problems.