If a₅ = 27 and d = 4, what is the 11th term?
Answer and explanation
Correct answer: 51
The governing AP principle is that moving from a known term aᵣ to another term aₙ changes the value by (n − r)d. Here the fifth term is 27 and the common difference is 4. From the fifth term to the eleventh term there are 11 − 5 = 6 equal intervals, not five or seven. Therefore a₁₁ = a₅ + (11 − 5)d = 27 + 6 × 4 = 27 + 24 = 51. Hence option C is correct. Finding the first term is unnecessary because a middle term has already been supplied. Option B would add only five differences, option D would add seven, and option A reflects a different counting or arithmetic error. Counting the intervals between the term numbers prevents the common off-by-one mistake.
Frequently asked questions
What is the correct answer to this question?
51
Why is this the correct answer?
The governing AP principle is that moving from a known term aᵣ to another term aₙ changes the value by (n − r)d. Here the fifth term is 27 and the common difference is 4. From the fifth term to the eleventh term there are 11 − 5 = 6 equal intervals, not five or seven. Therefore a₁₁ = a₅ + (11 − 5)d = 27 + 6 × 4 = 27 + 24 = 51. Hence option C is correct. Finding the first term is unnecessary because a middle term has already been supplied. Option B would add only five differences, option D would add seven, and option A reflects a different counting or arithmetic error. Counting the intervals between the term numbers prevents the common off-by-one mistake.
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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