Physics and Mathematics
Example 1 A.P.
Practice Questions with Step-by-Step Solutions
Question 1. Find the 12ᵗʰ term of the AP [3, 7, 11, …].
Step-by-Step Solution:
a = 3, d = 4, n = 12
[a₁₂ = 3 + (12 − 1) × 4]
[a₁₂ = 3 + 44 = 47]
Conclusion:
The 12ᵗʰ term is 47.
Question 2. Find the 20ᵗʰ term of the AP [−5, −2, 1, …].
Step-by-Step Solution:
a = −5, d = 3, n = 20
[a₂₀ = −5 + 19 × 3 = 52]
Conclusion:
The 20ᵗʰ term is 52.
Question 3. Find the nᵗʰ term of the AP with a = 7 and d = −2.
Step-by-Step Solution:
[aₙ = 7 + (n − 1)(−2)]
[aₙ = 9 − 2n]
Conclusion:
The nᵗʰ term is [9 − 2n].
Question 4. Find the 15ᵗʰ term of the AP [1/3, 4/3, 7/3, …].
Step-by-Step Solution:
a = 1/3, d = 1, n = 15
[a₁₅ = 1/3 + 14]
[a₁₅ = 43/3]
Conclusion:
The 15ᵗʰ term is 43/3.
Question 5. Find the 1ˢᵗ term using nᵗʰ term formula.
Step-by-Step Solution:
Substitute n = 1
[a₁ = a + (1 − 1)d = a]
Conclusion:
The first term is a.
Question 6. Find the 25ᵗʰ term of the AP [10, 8, 6, …].
Step-by-Step Solution:
a = 10, d = −2, n = 25
[a₂₅ = 10 + 24(−2)]
[a₂₅ = −38]
Conclusion:
The 25ᵗʰ term is −38.
Question 7. Find the nᵗʰ term of the AP [2, 2, 2, …].
Step-by-Step Solution:
a = 2, d = 0
[aₙ = 2]
Conclusion:
All terms are equal to 2.
Question 8. Find the 9ᵗʰ term of the AP [−1, −4, −7, …].
Step-by-Step Solution:
a = −1, d = −3, n = 9
[a₉ = −1 + 8(−3)]
[a₉ = −25]
Conclusion:
The 9ᵗʰ term is −25.
Question 9. Find the nᵗʰ term of the AP [5, 9, 13, …].
Step-by-Step Solution:
a = 5, d = 4
[aₙ = 5 + (n − 1)4 = 4n + 1]
Conclusion:
The nᵗʰ term is [4n + 1].
Question 10. Find the 30ᵗʰ term of the AP [1, −1, −3, …].
Step-by-Step Solution:
a = 1, d = −2, n = 30
[a₃₀ = 1 + 29(−2)]
[a₃₀ = −57]
Conclusion:
The 30ᵗʰ term is −57.
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