Kundali IQHome › Exam notes › UPSC NDA/NA › Sequences & Series
Sequences & Series
Mathematics
Useful for: UPSC NDA/NA
Overview
Sequences are ordered lists of numbers; arithmetic and geometric progressions have standard formulas for terms and sums.
Key points
- AP nth term: a + (n − 1)d; sum: n/2 [2a + (n − 1)d].
- GP nth term: a rⁿ⁻¹; sum: a(rⁿ − 1)/(r − 1) for r ≠ 1.
- Infinite GP sum = a/(1 − r) when |r| < 1.
- Sum of first n natural numbers = n(n + 1)/2.
- For positive numbers, AM ≥ GM.
- Sum of squares of first n natural numbers = n(n + 1)(2n + 1)/6.
Practice MCQs
From the perspective of definition and scope, which one of the following statements about Sequences & Series is correct?
- Sequences & Series has no exceptions or limitations in exam analysis.
- Sequences & Series questions reward a formula-first approach and accurate algebraic manipulation.
- Do not apply a memorized Sequences & Series formula without checking its conditions.
- Sequences & Series is unrelated to institutions, processes or real-world applications.
Read chapter notes · Similar questions
Show answer
Answer: (b) Sequences & Series questions reward a formula-first approach and accurate algebraic manipulation.. Sequences & Series questions reward a formula-first approach and accurate algebraic manipulation.
Consider the following statements on Sequences & Series, focusing on definition and scope: 1. Do not apply a memorized Sequences & Series formula without checking its conditions. 2. Sequences & Series questions reward a formula-first approach and accurate algebraic manipulation. Which of the statements given above is/are correct?
- 1 only
- 2 only
- Both 1 and 2
- Neither 1 nor 2
Read chapter notes · Similar questions
Show answer
Answer: (b) 2 only. Statement 2 is correct; Statement 1 is a common misconception.
More topics in this chapter
Notes and questions are written by Kundali IQ for practice. They are not official papers; always check the latest official notification for the syllabus and pattern.