Physics and Mathematics
Example 3 A.P.
Practice Questions with Step-by-Step Solutions
Question 21. Find the 16ᵗʰ term of the AP [6, 11, 16, …].
Step-by-Step Solution:
a = 6, d = 5, n = 16
[a₁₆ = 6 + (16 − 1) × 5]
[a₁₆ = 6 + 75 = 81]
Conclusion:
The 16ᵗʰ term is 81.
Question 22. Find the 50ᵗʰ term of the AP [2, 0, −2, …].
Step-by-Step Solution:
a = 2, d = −2, n = 50
[a₅₀ = 2 + 49(−2)]
[a₅₀ = −96]
Conclusion:
The 50ᵗʰ term is −96.
Question 23. Find the nᵗʰ term of the AP [1/5, 3/5, 5/5, …].
Step-by-Step Solution:
a = 1/5, d = 2/5
[aₙ = 1/5 + (n − 1) × 2/5]
[aₙ = (2n − 1)/5]
Conclusion:
The nᵗʰ term is [(2n − 1)/5].
Question 24. Find the 9ᵗʰ term of the AP [−7, −3, 1, …].
Step-by-Step Solution:
a = −7, d = 4, n = 9
[a₉ = −7 + 8 × 4]
[a₉ = 25]
Conclusion:
The 9ᵗʰ term is 25.
Question 25. Find the nᵗʰ term of the AP whose first term is 3/2 and common difference is −1/2.
Step-by-Step Solution:
a = 3/2, d = −1/2
[aₙ = 3/2 + (n − 1)(−1/2)]
[aₙ = (4 − n)/2]
Conclusion:
The nᵗʰ term is [(4 − n)/2].
Question 26. Find the 27ᵗʰ term of the AP [−10, −5, 0, …].
Step-by-Step Solution:
a = −10, d = 5, n = 27
[a₂₇ = −10 + 26 × 5]
[a₂₇ = 120]
Conclusion:
The 27ᵗʰ term is 120.
Question 27. Find the nᵗʰ term of the AP [9, 6, 3, …].
Step-by-Step Solution:
a = 9, d = −3
[aₙ = 9 + (n − 1)(−3)]
[aₙ = 12 − 3n]
Conclusion:
The nᵗʰ term is [12 − 3n].
Question 28. Find the 35ᵗʰ term of the AP [1/4, 5/4, 9/4, …].
Step-by-Step Solution:
a = 1/4, d = 1, n = 35
[a₃₅ = 1/4 + 34]
[a₃₅ = 137/4]
Conclusion:
The 35ᵗʰ term is 137/4.
Question 29. Find the 60ᵗʰ term of the AP [5, 10, 15, …].
Step-by-Step Solution:
a = 5, d = 5, n = 60
[a₆₀ = 5 + 59 × 5]
[a₆₀ = 300]
Conclusion:
The 60ᵗʰ term is 300.
Question 30. Find the nᵗʰ term of the AP whose first term is −7 and common difference is 2.
Step-by-Step Solution:
a = −7, d = 2
[aₙ = −7 + (n − 1)2]
[aₙ = 2n − 9]
Conclusion:
The nᵗʰ term is [2n − 9].
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