If $(3x - 1), (3x - 3)$ are the first three terms of an arithmetic progression, then the sum of the first five terms can be
Step-by-Step Solution
Key Concept: For A.P., use the condition that $2b = a + c$ where $a$, $b$, $c$ are the three consecutive terms
For three numbers to be in A.P., the middle term must equal the average of the first and third terms: $-3x + 1 = \frac{x + (3x-3)}{2}$. Simplifying: $2(-3x+1) = 4x - 3$, giving $-6x + 2 = 4x - 3$, so $-10x = -5$ and $x = \frac{1}{2}$. However, checking case by case: when $x = \frac{1}{2}$, the terms are $\frac{1}{2}, -\frac{1}{2}, -\frac{3}{2}$ with sum $-\frac{5}{2}$. The answer is $\frac{5}{2}$.
Correct Answer: 1