Which sequence is an arithmetic progression with (d=-5)?
Answer and explanation
Correct answer: (40,35,30,25,\ldots)
An arithmetic progression has one fixed common difference throughout the sequence. For a required difference of \\(d=-5\\), every next term must be exactly 5 less than the preceding term. The minus sign is important: the sequence must decrease by 5 each time, not increase by 5 or decrease by varying amounts.
For choice B, the consecutive differences are \\(35-40=-5\\), \\(30-35=-5\\), and \\(25-30=-5\\). Since the same value continues, it is an arithmetic progression with common difference \\(-5\\). Choice A has difference \\(+5\\), choice C changes by \\(-5,-6,-7\\), and choice D has differences \\(-5,-10,-5\\). Therefore only choice B satisfies the condition.
Frequently asked questions
What is the correct answer to this question?
(40,35,30,25,\ldots)
Why is this the correct answer?
An arithmetic progression has one fixed common difference throughout the sequence. For a required difference of \\(d=-5\\), every next term must be exactly 5 less than the preceding term. The minus sign is important: the sequence must decrease by 5 each time, not increase by 5 or decrease by varying amounts.
For choice B, the consecutive differences are \\(35-40=-5\\), \\(30-35=-5\\), and \\(25-30=-5\\). Since the same value continues, it is an arithmetic progression with common difference \\(-5\\). Choice A has difference \\(+5\\), choice C changes by \\(-5,-6,-7\\), and choice D has differences \\(-5,-10,-5\\). Therefore only choice B satisfies the condition.
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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