Which one of the following is not an A.P. (Arithmetic Progression)?

Question

Accepted Answer

**Question Statement:**  
Which one of the following is not an A.P. (Arithmetic Progression)?

**Options:**  
(a) 11, 7, 3, –1, –5  
(b) 0, –3, –6, –9  
(c) 3, 9, 19, 33, 51  
(d) 9, 13, 17, 21, 25

**Correct Answer:**  
(c) 3, 9, 19, 33, 51

**Title:**  
Identify Non-Arithmetic Progression

**Difficulty:**  
Easy

**Section:**  
Quantitative Aptitude

**Category:**  
Algebra

**Topic:**  
Sequence and Series (AP/GP/HP)

**Tags:**  
Arithmetic Progression, Sequence Analysis

**Solution Language:**  
To determine whether a sequence is an A.P., the difference between consecutive terms must remain constant. Let's analyze each option:

- **Option (a):** $$11 - 7 = 4$$, $$7 - 3 = 4$$, $$3 - (-1) = 4$$, $$(-1) - (-5) = 4$$. The difference is constant ($$4$$), so this is an A.P.

- **Option (b):** $$0 - (-3) = 3$$, $$(-3) - (-6) = 3$$, $$(-6) - (-9) = 3$$. The difference is constant ($$3$$), so this is an A.P.

- **Option (c):** $$9 - 3 = 6$$, $$19 - 9 = 10$$, $$33 - 19 = 14$$, $$51 - 33 = 18$$. The differences are not constant ($$6, 10, 14, 18$$), so this is **not an A.P.**

- **Option (d):** $$13 - 9 = 4$$, $$17 - 13 = 4$$, $$21 - 17 = 4$$, $$25 - 21 = 4$$. The difference is constant ($$4$$), so this is an A.P.

Thus, the sequence in **option (c)** is not an A.P.

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