In the sequence (70, 64, 58, 52, ...), what are the next term and d, respectively?
Answer and explanation
Correct answer: 46 and −6
For an arithmetic progression, the common difference d is the same subtraction between every pair of consecutive terms. Here, 64−70=−6, 58−64=−6, and 52−58=−6, so d=−6. To obtain the next term, add this difference to the last known term: 52+(−6)=46. Therefore the next term and d, in the requested order, are 46 and −6, so option A is correct. Option B has the wrong sign for the difference and would make the sequence increase. Options C and D repeat terms already present rather than giving the next term. The negative difference correctly reflects that the sequence decreases by 6 each time.
Frequently asked questions
What is the correct answer to this question?
46 and −6
Why is this the correct answer?
For an arithmetic progression, the common difference d is the same subtraction between every pair of consecutive terms. Here, 64−70=−6, 58−64=−6, and 52−58=−6, so d=−6. To obtain the next term, add this difference to the last known term: 52+(−6)=46. Therefore the next term and d, in the requested order, are 46 and −6, so option A is correct. Option B has the wrong sign for the difference and would make the sequence increase. Options C and D repeat terms already present rather than giving the next term. The negative difference correctly reflects that the sequence decreases by 6 each time.
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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