How to Solve Sequences and Series Problems Easily
Practice Paper: Sequences and Series

FAQs on Practice Paper: Sequences and Series
1. What is the difference between a sequence and a series?
Sequences are ordered lists of numbers, while series represent the sum of the terms in a sequence.
Key differences include:
- Sequence: Each number is called a term.
- Series: The sum of sequence terms (e.g., arithmetic series, geometric series).
- Sequences have an order; series focus on their total.
2. What is the general formula for the nth term of an arithmetic progression (AP)?
The nth term of an arithmetic progression (AP) is found using the formula:
aₙ = a₁ + (n – 1)d
- aₙ: nth term
- a₁: first term
- d: common difference
- n: term number
3. How do you find the sum of the first n terms of a geometric progression (GP)?
The sum of the first n terms of a geometric progression (GP) is calculated by:
Sₙ = a₁(1 – rⁿ)/(1 – r) (when r ≠ 1)
- Sₙ: sum of first n terms
- a₁: first term
- r: common ratio
- n: number of terms
4. Define arithmetic mean and give its formula.
The arithmetic mean (AM) between two numbers is the average value, and is a crucial concept in sequences and statistics.
- Formula: AM = (a + b)/2
- It is the central value between a and b in an arithmetic sequence.
5. What are the important properties of geometric progression (GP)?
The key properties of geometric progression (GP) help in finding sums and terms:
- Each term after the first is obtained by multiplying the previous term by a fixed common ratio (r).
- If all terms of a GP are multiplied/divided by a non-zero constant, the new sequence is also a GP.
- Product of equidistant terms from beginning and end is constant.
6. How do you identify if a sequence is an arithmetic progression?
A sequence is an arithmetic progression (AP) if the difference between consecutive terms is always the same.
- Calculate common difference (d):
d = a₂ – a₁, a₃ – a₂, etc. - If d remains constant, it’s an AP.
7. What is the formula for the sum of the first n natural numbers?
The summation of the first n natural numbers uses the formula:
S = n(n + 1)/2
- This is a fundamental result used for progressions, series calculations, and mathematical induction proofs.
- Applicable for CBSE board and competitive exams.
8. State the applications of sequences and series in real life.
Sequences and series are widely used in various real-life situations:
- Financial calculations like compound interest, EMI, annuities
- Population growth and predictions
- Engineering problems involving patterns and signals
- Computer programming for loops and iterations
9. What is the sum to infinity of a geometric series?
For a geometric series with a common ratio |r| < 1, the sum to infinity is:
S_∞ = a₁ / (1 – r)
- a₁: first term
- r: common ratio with |r| < 1
10. If the nth term of a sequence is 2n + 3, find the 5th term.
To find the 5th term, substitute n = 5 into the formula:
- nth term: aₙ = 2n + 3
- a₅ = 2 × 5 + 3 = 13
11. Explain the difference between finite and infinite series.
A finite series has a limited number of terms, while an infinite series continues endlessly.
- Finite: Example – 1 + 2 + 3 + ... + 10
- Infinite: Example – 1 + 1/2 + 1/4 + 1/8 + ...






















