Physics and Mathematics
Example 4 A.P.
Practice Questions with Step-by-Step Solutions
Question 31. Find the 24ᵗʰ term of the AP [7, 12, 17, …].
Step-by-Step Solution:
a = 7, d = 5, n = 24
[a₂₄ = 7 + (24 − 1) × 5]
[a₂₄ = 7 + 115 = 122]
Conclusion:
The 24ᵗʰ term is 122.
Question 32. Find the 75ᵗʰ term of the AP [10, 8, 6, …].
Step-by-Step Solution:
a = 10, d = −2, n = 75
[a₇₅ = 10 + 74(−2)]
[a₇₅ = −138]
Conclusion:
The 75ᵗʰ term is −138.
Question 33. Find the nᵗʰ term of the AP [3/2, 2, 5/2, …].
Step-by-Step Solution:
a = 3/2, d = 1/2
[aₙ = 3/2 + (n − 1)(1/2)]
[aₙ = (n + 2)/2]
Conclusion:
The nᵗʰ term is [(n + 2)/2].
Question 34. Find the 13ᵗʰ term of the AP [−9, −4, 1, …].
Step-by-Step Solution:
a = −9, d = 5, n = 13
[a₁₃ = −9 + 12 × 5]
[a₁₃ = 51]
Conclusion:
The 13ᵗʰ term is 51.
Question 35. Find the nᵗʰ term of the AP whose first term is −5/2 and common difference is 3/2.
Step-by-Step Solution:
a = −5/2, d = 3/2
[aₙ = −5/2 + (n − 1)(3/2)]
[aₙ = (3n − 8)/2]
Conclusion:
The nᵗʰ term is [(3n − 8)/2].
Question 36. Find the 90ᵗʰ term of the AP [1, 1, 1, …].
Step-by-Step Solution:
a = 1, d = 0, n = 90
[a₉₀ = 1]
Conclusion:
The 90ᵗʰ term is 1.
Question 37. Find the nᵗʰ term of the AP [11, 7, 3, …].
Step-by-Step Solution:
a = 11, d = −4
[aₙ = 11 + (n − 1)(−4)]
[aₙ = 15 − 4n]
Conclusion:
The nᵗʰ term is [15 − 4n].
Question 38. Find the 17ᵗʰ term of the AP [5/3, 8/3, 11/3, …].
Step-by-Step Solution:
a = 5/3, d = 1, n = 17
[a₁₇ = 5/3 + 16]
[a₁₇ = 53/3]
Conclusion:
The 17ᵗʰ term is 53/3.
Question 39. Find the 120ᵗʰ term of the AP [−3, 0, 3, …].
Step-by-Step Solution:
a = −3, d = 3, n = 120
[a₁₂₀ = −3 + 119 × 3]
[a₁₂₀ = 354]
Conclusion:
The 120ᵗʰ term is 354.
Question 40. Find the nᵗʰ term of the AP whose first term is 4 and common difference is −7.
Step-by-Step Solution:
a = 4, d = −7
[aₙ = 4 + (n − 1)(−7)]
[aₙ = 11 − 7n]
Conclusion:
The nᵗʰ term is [11 − 7n].
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