In an AP, a₁₃ = 2a₅ + 9 and a₅ = 25. What is a₂₉?
Answer and explanation
Correct answer: 127
The governing formula for the nth term of an arithmetic progression is aₙ = aₘ + (n − m)d, where d is the common difference. First, use the given relation: a₁₃ = 2a₅ + 9 = 2(25) + 9 = 59. Since a₁₃ = a₅ + 8d, we get 59 = 25 + 8d, so 8d = 34 and d = 17/4. Now move from the fifth term to the twenty-ninth term, which is 24 steps: a₂₉ = a₅ + 24d = 25 + 24(17/4) = 25 + 102 = 127. Therefore, option A is correct. The other choices result from using an incorrect number of common-difference steps or an arithmetic error.
Frequently asked questions
What is the correct answer to this question?
127
Why is this the correct answer?
The governing formula for the nth term of an arithmetic progression is aₙ = aₘ + (n − m)d, where d is the common difference. First, use the given relation: a₁₃ = 2a₅ + 9 = 2(25) + 9 = 59. Since a₁₃ = a₅ + 8d, we get 59 = 25 + 8d, so 8d = 34 and d = 17/4. Now move from the fifth term to the twenty-ninth term, which is 24 steps: a₂₉ = a₅ + 24d = 25 + 24(17/4) = 25 + 102 = 127. Therefore, option A is correct. The other choices result from using an incorrect number of common-difference steps or an arithmetic error.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the $n$th term of an AP.
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