The numbers 14, m, and 50 are consecutive terms of an arithmetic progression (AP). What are m and d?
Answer and explanation
Correct answer: m = 32, d = 18
The governing property is that consecutive terms of an AP have equal differences. Therefore, m − 14 must equal 50 − m. Solving gives 2m = 64, so m = 32. The common difference is then d = m − 14 = 32 − 14 = 18; it also agrees with 50 − 32 = 18. Hence option B is correct. Option A incorrectly uses 30 as the middle term and consequently gets a difference of 16. Options C and D place the middle term too high, so their two successive differences are not equal: 20 and 16 for C, and 22 and 14 for D. The arithmetic-mean rule, m = (14 + 50)/2, provides the same result.
Frequently asked questions
What is the correct answer to this question?
m = 32, d = 18
Why is this the correct answer?
The governing property is that consecutive terms of an AP have equal differences. Therefore, m − 14 must equal 50 − m. Solving gives 2m = 64, so m = 32. The common difference is then d = m − 14 = 32 − 14 = 18; it also agrees with 50 − 32 = 18. Hence option B is correct. Option A incorrectly uses 30 as the middle term and consequently gets a difference of 16. Options C and D place the middle term too high, so their two successive differences are not equal: 20 and 16 for C, and 22 and 14 for D. The arithmetic-mean rule, m = (14 + 50)/2, provides the same result.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Introduction to APs and common difference..
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