CUET PG 2026 — Mathematics PYQ

Step 1: Check the Assertion

For a sequence to be an Arithmetic Progression (AP), the difference between consecutive terms must be constant ($d=a_2-a_1=a_3-a_2$).

Let's check the differences:

• $d_1=-\frac{1}{2}-\frac{1}{3}=\frac{-3-2}{6}=-\frac{5}{6}$

• $d_2=\frac{3}{4}-(-\frac{1}{2})=\frac{3}{4}+\frac{2}{4}=\frac{5}{4}$

Since $-\frac{5}{6}\ne \frac{5}{4}$, the common difference is not constant. Therefore, the sequence is not an AP.

Interestingly, if you check the ratio:

• $r=\frac{-1/2}{1/3}=-\frac{3}{2}$

• $r=\frac{3/4}{-1/2}=-\frac{3}{2}$

  The sequence is actually a Geometric Progression (GP).

• Assertion is False.

Step 2: Check the Reason

A constant sequence (e.g., $5,5,5,\dots$) is an AP with common difference $d=0$ and a GP with common ratio $r=1$. While it is a primary example of a sequence that is both, it is generally considered the only non-trivial case in standard real-number sequences.

• Reason is True.

Conclusion:

Since the Assertion is false and the Reason is true, we match this to option (d).

Correct Option: (d) Assertion is false, but Reason is true.