Complete Guide to CDS Arithmetic Progression Solved Examples 2027

Arithmetic Progression (AP) is a foundational topic in the CDS Mathematics syllabus, frequently accounting for 3-5 questions. To excel, you must master the nth term formula (a_n = a + (n-1)d) and sum of n terms (S_n = n/2[2a + (n-1)d]). Practice consistent daily calculation to ensure accuracy under time pressure.

What is the Exam?

The Combined Defence Services (CDS) examination is conducted twice a year by the Union Public Service Commission (UPSC). It serves as the gateway for induction into the Indian Military Academy (IMA), Indian Naval Academy (INA), Air Force Academy (AFA), and Officers Training Academy (OTA). We at Exam Bhai view the CDS exam as a rigorous test of both physical aptitude and intellectual endurance, requiring a highly structured approach to the Mathematics paper.

Key Highlights 2026

• Exam Conducted by: Union Public Service Commission (UPSC)
• Exam Level: National Level
• Mode: Offline (Pen and Paper)
• Selection Process: Written Exam followed by SSB Interview
• Frequency: Twice a year
• Language: English and Hindi

Syllabus 2026

Exam Pattern

The Mathematics paper for IMA, INA, and AFA consists of 100 questions carrying 100 marks. Each incorrect answer attracts a negative marking of one-third. To gain an edge, you should practice high-yield CDS 2027 mock tests on Exam Bhai.

Eligibility Criteria

As specified by the official UPSC portal (upsc.gov.in), candidates must be Indian citizens, hold a graduate degree, and meet stringent age and physical standards. IMA/INA/AFA candidates must be unmarried, while specific age brackets are enforced for each academy based on the year of notification.

Application Process

Candidates must register via the UPSC online portal. The process involves Part I (Registration) and Part II (Fee payment and centre selection). Ensure all details align with your official documents to avoid disqualification during the document verification stage.

Preparation Strategy

Mathematics requires conceptual clarity. We at Exam Bhai recommend focusing on Arithmetic Progression because it is highly scoring.

1. Master the basics: Understand the common difference (d) and first term (a).
2. Solve previous year questions (PYQs) to understand the pattern.
3. Utilize our curated study materials for CDS 2027 to refine your speed.
4. Simulate exam conditions; when you attempt timed CDS 2027 sectional tests, treat them like the real test.

Solved Examples

Example 1: Find the 10th term of the AP: 2, 7, 12, ...

• Solution: Here, a = 2, d = 5. Formula: a_n = a + (n-1)d.
• 10th term = 2 + (10-1)5 = 2 + 45 = 47.

Example 2: Find the sum of the first 20 terms of the AP: 1, 3, 5, 7, ...

• Solution: a = 1, d = 2. Formula: S_n = n/2[2a + (n-1)d].
• S_20 = 20/2 [2(1) + (19)2] = 10 [2 + 38] = 10 * 40 = 400.

Cut-Off Trends

Historical data from upsc.gov.in suggests that the cut-off for the written exam typically ranges between 110-135 marks for IMA, depending on the difficulty level of the paper. We advise targeting at least 150 to ensure a safety buffer.

Frequently Asked Questions

Q1: How many questions appear from AP in CDS math? A: Typically 2 to 4 questions. It is a high-yield, low-effort topic.

Q2: Is the formula for GP different from AP? A: Yes, GP deals with a common ratio (r), while AP deals with a common difference (d).

Q3: Are calculators allowed? A: No, electronic devices are strictly prohibited in the exam hall.

Q4: Can I skip Mathematics if applying for OTA? A: Yes, the OTA exam only includes English and General Knowledge.

Q5: How should I handle negative marking? A: Focus on accuracy over quantity. Only mark questions where you are 80% confident.

Q6: Is NCERT enough for AP? A: NCERT is excellent for basics, but you must supplement it with advanced practice sets to meet the CDS difficulty level.