In an AP, a₁₃ = 65 and a₂₁ = 113. What is a₆?
Answer and explanation
Correct answer: 23
Use the fact that the difference between two AP terms equals the number of intervals multiplied by the common difference. From the 13th to the 21st term there are eight intervals, so 113 − 65 = 48 = 8d, which gives d = 6. The 6th term is seven intervals before the 13th term. Therefore a₆ = a₁₃ − 7d = 65 − 7 × 6 = 65 − 42 = 23. Hence option C is correct. Moving backward requires subtraction, not addition. The other choices result from using six or eight intervals, or from an incorrect sign while moving to an earlier term.
Frequently asked questions
What is the correct answer to this question?
23
Why is this the correct answer?
Use the fact that the difference between two AP terms equals the number of intervals multiplied by the common difference. From the 13th to the 21st term there are eight intervals, so 113 − 65 = 48 = 8d, which gives d = 6. The 6th term is seven intervals before the 13th term. Therefore a₆ = a₁₃ − 7d = 65 − 7 × 6 = 65 − 42 = 23. Hence option C is correct. Moving backward requires subtraction, not addition. The other choices result from using six or eight intervals, or from an incorrect sign while moving to an earlier 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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