Physics and Mathematics
Example 2 A.P.
Practice Questions with Step-by-Step Solutions
Question 11. Find the 18ᵗʰ term of the AP [4, 9, 14, …].
Step-by-Step Solution:
a = 4, d = 5, n = 18
[a₁₈ = 4 + (18 − 1) × 5]
[a₁₈ = 4 + 85 = 89]
Conclusion:
The 18ᵗʰ term is 89.
Question 12. Find the 40ᵗʰ term of the AP [7, 7, 7, …].
Step-by-Step Solution:
a = 7, d = 0, n = 40
[a₄₀ = 7 + 39 × 0 = 7]
Conclusion:
The 40ᵗʰ term is 7.
Question 13. Find the nᵗʰ term of the AP [−3, −6, −9, …].
Step-by-Step Solution:
a = −3, d = −3
[aₙ = −3 + (n − 1)(−3)]
[aₙ = −3n]
Conclusion:
The nᵗʰ term is [−3n].
Question 14. Find the 11ᵗʰ term of the AP [1/2, 3/2, 5/2, …].
Step-by-Step Solution:
a = 1/2, d = 1, n = 11
[a₁₁ = 1/2 + 10]
[a₁₁ = 21/2]
Conclusion:
The 11ᵗʰ term is 21/2.
Question 15. Find the nᵗʰ term of the AP whose first term is 10 and common difference is −4.
Step-by-Step Solution:
a = 10, d = −4
[aₙ = 10 + (n − 1)(−4)]
[aₙ = 14 − 4n]
Conclusion:
The nᵗʰ term is [14 − 4n].
Question 16. Find the 21ˢᵗ term of the AP [−2, 1, 4, …].
Step-by-Step Solution:
a = −2, d = 3, n = 21
[a₂₁ = −2 + 20 × 3]
[a₂₁ = 58]
Conclusion:
The 21ˢᵗ term is 58.
Question 17. Find the nᵗʰ term of the AP [8, 5, 2, …].
Step-by-Step Solution:
a = 8, d = −3
[aₙ = 8 + (n − 1)(−3)]
[aₙ = 11 − 3n]
Conclusion:
The nᵗʰ term is [11 − 3n].
Question 18. Find the 14ᵗʰ term of the AP [3/4, 7/4, 11/4, …].
Step-by-Step Solution:
a = 3/4, d = 1, n = 14
[a₁₄ = 3/4 + 13]
[a₁₄ = 55/4]
Conclusion:
The 14ᵗʰ term is 55/4.
Question 19. Find the 100ᵗʰ term of the AP [1, 4, 7, …].
Step-by-Step Solution:
a = 1, d = 3, n = 100
[a₁₀₀ = 1 + 99 × 3]
[a₁₀₀ = 298]
Conclusion:
The 100ᵗʰ term is 298.
Question 20. Find the nᵗʰ term of the AP whose first term is −1 and common difference is 5.
Step-by-Step Solution:
a = −1, d = 5
[aₙ = −1 + (n − 1)5]
[aₙ = 5n − 6]
Conclusion:
The nᵗʰ term is [5n − 6].
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