Sequences – Algebra MCQs

By: Prof. Dr. Fazal Rehman Shamil | Last updated: January 31, 2025

\[
\textbf{MCQs on Sequences in Algebra with Answers}
\]

\[
\textbf{Q1: What is the common difference in the arithmetic sequence: } 3, 7, 11, 15, \dots?
\]
\[
\text{(A) } 3 \quad \text{(B) } 4 \quad \text{(C) } 5 \quad \text{(D) } 7
\]
\[
\textbf{Answer: (B) } 4
\]

\[
\textbf{Q2: What is the nth term formula for an arithmetic sequence with the first term 2 and common difference 5?}
\]
\[
\text{(A) } a_n = 5n – 3 \quad \text{(B) } a_n = 5n + 2 \quad \text{(C) } a_n = 2n + 5 \quad \text{(D) } a_n = 2n + 5
\]
\[
\textbf{Answer: (D) } a_n = 5n + 2
\]

\[
\textbf{Q3: What is the sum of the first 10 terms of the arithmetic sequence: 2, 5, 8, 11, \dots?}
\]
\[
\text{(A) } 150 \quad \text{(B) } 130 \quad \text{(C) } 120 \quad \text{(D) } 140
\]
\[
\textbf{Answer: (C) } 120
\]

\[
\textbf{Q4: What is the general form of a geometric sequence?}
\]
\[
\text{(A) } a_n = a_1 + (n-1) \cdot d \quad \text{(B) } a_n = a_1 \cdot r^{n-1} \quad \text{(C) } a_n = a_1 \cdot (n-1) \quad \text{(D) } a_n = a_1 + r^{n}
\]
\[
\textbf{Answer: (B) } a_n = a_1 \cdot r^{n-1}
\]

\[
\textbf{Q5: If the first term of a geometric sequence is 3 and the common ratio is 2, what is the 4th term?}
\]
\[
\text{(A) } 24 \quad \text{(B) } 24 \quad \text{(C) } 48 \quad \text{(D) } 32
\]
\[
\textbf{Answer: (A) } 24
\]

\[
\textbf{Q6: Which of the following is the sum formula for an arithmetic series?}
\]
\[
\text{(A) } S_n = \frac{n}{2} \cdot (a_1 + a_n) \quad \text{(B) } S_n = \frac{n}{2} \cdot (a_1 \cdot a_n) \quad \text{(C) } S_n = a_1 + a_2 \cdots a_n \quad \text{(D) } S_n = a_1 + \cdots + a_n
\]
\[
\textbf{Answer: (A) } S_n = \frac{n}{2} \cdot (a_1 + a_n)
\]

\[
\textbf{Q7: What is the sum of the first 6 terms of the geometric sequence: 3, 6, 12, 24, \dots?}
\]
\[
\text{(A) } 93 \quad \text{(B) } 91 \quad \text{(C) } 90 \quad \text{(D) } 95
\]
\[
\textbf{Answer: (C) } 90
\]

\[
\textbf{Q8: In an arithmetic sequence, if the first term is 5 and the 5th term is 25, what is the common difference?}
\]
\[
\text{(A) } 4 \quad \text{(B) } 5 \quad \text{(C) } 6 \quad \text{(D) } 7
\]
\[
\textbf{Answer: (B) } 5
\]

\[
\textbf{Q9: Which of the following is the general formula for the nth term of a sequence?}
\]
\[
\text{(A) } a_n = a_1 + (n-1) \cdot d \quad \text{(B) } a_n = a_1 \cdot r^n \quad \text{(C) } a_n = n + a_1 \quad \text{(D) } a_n = a_1 + r \cdot n
\]
\[
\textbf{Answer: (A) } a_n = a_1 + (n-1) \cdot d
\]

\[
\textbf{Q10: If a sequence is defined as \( a_n = 2^n \), what is the 5th term?}
\]
\[
\text{(A) } 32 \quad \text{(B) } 16 \quad \text{(C) } 64 \quad \text{(D) } 8
\]
\[
\textbf{Answer: (A) } 32
\]

More MCQs on Algebra (Collected from Past Papers)

1. Elementary Algebra – MCQs
2. Algebraic Expressions – MCQs
3. Algebraic Identities – MCQs
4. Commutative Algebra – MCQs
5. Linear Equations – MCQs
6. Graphing Linear Equations – MCQs
7. Inequalities in Algebra – MCQs
8. Absolute Value Inequalities – MCQs
9. Exponent – MCQs
10. Exponential Functions – MCQs
11. Logarithms – MCQs
12. Polynomials – MCQs
13. Factoring Methods – MCQs
14. Polynomial Arithmetic – MCQs
15. Quadratic Equation – MCQs
16. Linear Algebra – MCQs
17. Matrices in Algebra – MCQs
18. Functions in Algebra – MCQs
19. Sequences in Algebra – MCQs
20. Arithmetic in Algebra – MCQs
21. Combining Like Terms in Algebra – MCQs
22. Abstract Algebra – MCQs
23. Sets in Algebra – MCQs
24. Algebra Calculator – MCQs