Mathematics Sequences and Series MCQS Online Preparation Sample Paper Questions with Answer
Understanding Mathematics Sequences and Series is essential for success in the ECAT Engineering Entry Test Mathematics section. This topic covers numerical patterns, progressions, arithmetic and geometric sequences, summations, and convergence tests. Mathematics Sequences and Series MCQs frequently appear in the ECAT exam, testing students’ analytical and problem-solving skills.
At Nokryan.com, we provide free ECAT online preparation, including sample papers, practice questions, and detailed answers. This guide offers comprehensive Sequences and Series MCQs, helping students build a strong mathematical foundation and perform well on the test.
Key Concepts in Sequences and Series
1. Understanding Sequences and Series
- A sequence is an ordered list of numbers following a specific pattern.
- A series is the sum of the terms of a sequence.
- The two most common types of sequences are arithmetic sequences (A.P.) and geometric sequences (G.P.).
2. Arithmetic Sequences (A.P.)
- The difference between consecutive terms is constant (common difference ‘d’).
- The formula for the nth term of an A.P.: an = a + (n-1)d
- The formula for the sum of n terms of an A.P.: Sn = n/2 [ 2a +( n-1 )d ]
3. Geometric Sequences (G.P.)
- Each term is obtained by multiplying the previous term by a constant ratio (r).
- The formula for the nth term of a G.P.: Tn = a r(n-1)
- The formula for the sum of n terms of a G.P.: Sn = a(rn – 1) / (r – 1), r ≠1
4. Special Types of Series
- Harmonic Series: Reciprocal of an arithmetic sequence.
- Infinite Geometric Series: If | r | < 1, ts n S = a/ (1-r)
ECAT Mathematics Sequences and Series MCQs
1. The sum of n term of a G.P is
- 2ab/ a + b correct
- A+ b/2
- n/2[2a + (n-1)d]
- A(1-r)/1-r
2. if a, d, and Sn are the first terms, the common difference, and the sum of the first n terms of the series, then Sn =
- n/2[a + (n-1)d]
- a + (n-1)d
- n/2[2a + (n-1)d] correct
- n[2a + (n-1)d]
3. the common ratio of a geometric sequence cannot be
- 3
- 0 correct
- 2
- 1
4. A function whose domain is the set of natural numbers is called the
- Series
- Identity function
- Sequence correct
- Onto function
5. the second term of the sequence with the general term n2-4/2 is
- 3
- 1
- 0 correct
- -3
6. the A.P whose nth term is 2n-1 is
- 2,3,5… correct
- 5,3,1…,
- 1,3,5….
- 1,3,6….
7. if n is total number of arithmetic means between a and b the formula of mth arithmetic mean between a and b is
- a +m(a-b)/n+1
- a +n(b-a)/n+1
- none of these
- a +m(b-a)/n+1 correct
8. the fifth term and the nth term of the A.P. 1,5….are
- 17,4n-3 correct
- 17,4n
- 17,3n-4
- 4n-3,17
9. The difference of two consecutive terms of an arithmetic sequence is called its:
- Common ratio
- Arithmetic mean
- Common difference correct
- Geometric mean
10. The next two terms of the sequence 1,3,7,15,31,…… are
- 102, 188
- 112, 144
- None of these correct
- 112, 228
11. A number A is said to be the arithmetic mean between two numbers a and b if a, A, b is
- Not a sequence
- G P
- A sequence
- A.P correct
12. A1 A2,…., An are said to be n arithmetic means between a and b if a, A1 A2,…., An, b is
- A sequence
- Not a sequence
- G P
- A.P correct
13. the arithmetic mean between a and b is
- a +b/ 2 correct
- ±√ab
- a -b/ 2
- b –a/2
14. The series obtained by adding the terms of an arithmetic sequence is called the
- Infinite series
- Harmonic series
- Arithmetic correct
- Geometric series
15. the 7th tern of an arithmetic sequence whose first term is 2 and whose common difference is zero is
- 0
- 2
- 7 correct
- 14
16. the common difference of the sequence 5,8,11,14,…..is
- 3 correct
- -3
- 0
- 1
17. A sequence in which any term minus its immediate previous term gives a constant is called the
- Arithmetic sequence correct
- Complex sequence
- Harmonic sequence
- Geometric sequence
18. A sequence in which any term divided by its immediate previous term is called the
- Common Ratio correct
- Arithmetic mean
- Mean common
- Arithmetic progression
19. 2,4,6,8,10,12,….. is
- G.P
- A.P
- Arithmetic series correct
- Geometric series
20. the general term of a sequence is denoted by
- an
- na
- Sn correct
- n
21. nth term of A.P. is
- a1 + (n – 1) d correct
- none of these
- a + nd
- a + d/n
22. 1,8,15,22,29,36,…. Is
- Geometric series
- Arithmetic series
- A.P correct
- G.P
23. the nth of an A.P is ½(3-n) ,the first three terns are
- 3,2,1
- 1,2,1
- 1,1/2,0 correct
- 1,2,3
24. the arithmetic mean between 2+√2 and 2-√2 is
- 2 correct
- 4
- 0
- √2
25. A sequence in which any term divided by its immediate previous term gives a constant is called the
- Real sequence
- Complex sequence
- Geometric sequence correct
- Arithmetic sequence
Conclusion
Mastering Mathematics Sequences and Series is essential for success in ECAT Engineering Entry Test Mathematics. Understanding arithmetic and geometric sequences, their sums, and solving related MCQs can significantly boost performance. Practicing with solved MCQs, past papers, and expert guides will strengthen your problem-solving skills.
For more ECAT online preparation, sample papers, and study resources, visit Nokryan.com and enhance your exam readiness today!