Sequence and Series
Geometric Progression
JEE Main 2019
Grade 11
Question:
If $a, b, c$ are three distinct real numbers in G.P. and $a + b + c = xb$, then $x$ cannot be:
(1) $4$
(2) $-2$
(3) $2$
(4) $5$
Step-by-Step Solution
Key Concept: Write $a = b/r, c = br$ so $x = 1/r + 1 + r$. For $r > 0$: $r + 1/r \geq 2$ so $x \geq 3$. For $r < 0$: $r + 1/r \leq -2$ so $x \leq -1$. Identify which option falls outside these ranges.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (3)