Find the General Term of a Sequence (Tn) – Practice Questions for CAT/XAT
July 17, 2024 2025-07-17 14:35Find the General Term of a Sequence (Tn) – Practice Questions for CAT/XAT
Find the General Term of a Sequence (Tn) – Practice Questions for CAT/XAT
Amiya Kumar 🧠 Find the General Term \(T_n\) – CAT/XAT Series Practice
In these 5 carefully curated sets, you're given the first few terms of a series. Your task is to find the general term and answer other related questions. Click to reveal the solutions below each question set.
🔷 Set 1 (Quadratic)
Given terms: 6, 12, 22, 36, 54, 76,..
- Find the general term \(T_n\)
- What is the degree of the general term?
- What is the degree of the summation formula \(\sum T_n\)?
- What is the next term (6th)?
- Find the 10th term
Click to see solution and answers
\( T_n = 2n^2 + 4 \)
- Degree of general term: 2
- Degree of summation: 3
- 6th term: \( T_6 = 2(36) + 4 = \boxed{76} \)
- 10th term: \( T_{10} = 2(100) + 4 = \boxed{204} \)
🔷 Set 2 (Quadratic)
Given terms: 7, 14, 25, 40, 59, 82,..
- Find the general term \(T_n\)
- What is the degree of the general term?
- What is the degree of the summation formula \(\sum T_n\)?
- What is the next term (6th)?
- Find the 10th term
Click to see solution and answers
\( T_n = 2n^2 + n + 4 \)
- Degree of general term: 2
- Degree of summation: 3
- 6th term: \( T_6 = 2(36) + 6 + 4 = \boxed{76} \)
- 10th term: \( T_{10} = 2(100) + 10 + 4 = \boxed{214} \)
🔶 Set 3 (Cubic)
Given terms: 4, 14, 38, 82, 152, 254,..
- Find the general term \(T_n\)
- What is the degree of the general term?
- What is the degree of the summation formula \(\sum T_n\)?
- What is the next term (6th)?
- Find the 10th term
Click to see solution and answers
\( T_n = n^3 + n^2 + 2 \)
- Degree of general term: 3
- Degree of summation: 4
- 6th term: \( T_6 = 216 + 36 + 2 = \boxed{254} \)
- 10th term: \( T_{10} = 1000 + 100 + 2 = \boxed{1102} \)
🔶 Set 4 (Cubic)
Given terms: 1, 6, 29, 82, 177, 326,..
- Find the general term \(T_n\)
- What is the degree of the general term?
- What is the degree of the summation formula \(\sum T_n\)?
- What is the next term (6th)?
- Find the 10th term
Click to see solution and answers
\( T_n = 2n^3 - 3n^2 + 2 \)
- Degree of general term: 3
- Degree of summation: 4
- 6th term: \( T_6 = 432 - 108 + 2 = \boxed{326} \)
- 10th term: \( T_{10} = 2000 - 300 + 2 = \boxed{1702} \)
🔺 Set 5 (Quartic)
Given terms: 2, 17, 82, 257, 626, 1297,..
- Find the general term \(T_n\)
- What is the degree of the general term?
- What is the degree of the summation formula \(\sum T_n\)?
- Find the next term (6th term)
- Find the 10th term
- Briefly explain how the degree was identified
- Comment on the nature of growth of the sequence (Linear / Polynomial / Exponential)
Click to see solution and answers
\( T_n = n^4 + 1 \)
- Degree of general term: 4
- Degree of summation: 5
- 6th term: \( T_6 = 1296 + 1 = \boxed{1297} \)
- 10th term: \( T_{10} = 10000 + 1 = \boxed{10001} \)
- Explanation: Repeated difference method shows 4th difference as constant ⇒ degree = 4
- Growth Type: Polynomial (quartic) – grows rapidly but slower than exponential
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