In an AP, a₁₂ = 5a₄ − 6 and a₄ = 16. What is a₂₄?
Answer and explanation
Correct answer: 161
For an arithmetic progression, the difference between two terms equals the difference in their indices multiplied by the common difference: a₁₂ − a₄ = 8d. The given value a₄ = 16 first gives a₁₂ = 5(16) − 6 = 80 − 6 = 74. Hence 74 − 16 = 8d, so 58 = 8d and d = 29/4. To reach a₂₄ from a₄, there are 24 − 4 = 20 equal steps. Therefore a₂₄ = a₄ + 20d = 16 + 20(29/4) = 16 + 145 = 161. Thus option C is correct. Options A, B, and D do not satisfy the correct twenty-step movement from the fourth term.
Frequently asked questions
What is the correct answer to this question?
161
Why is this the correct answer?
For an arithmetic progression, the difference between two terms equals the difference in their indices multiplied by the common difference: a₁₂ − a₄ = 8d. The given value a₄ = 16 first gives a₁₂ = 5(16) − 6 = 80 − 6 = 74. Hence 74 − 16 = 8d, so 58 = 8d and d = 29/4. To reach a₂₄ from a₄, there are 24 − 4 = 20 equal steps. Therefore a₂₄ = a₄ + 20d = 16 + 20(29/4) = 16 + 145 = 161. Thus option C is correct. Options A, B, and D do not satisfy the correct twenty-step movement from the fourth term.
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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