If each term of 6, 11, 16, … is multiplied by 2 and 3 is added, what will be the common difference of the new sequence?
Answer and explanation
Correct answer: 10
The original sequence is an arithmetic progression because consecutive terms differ by 11 − 6 = 5 and 16 − 11 = 5. If each original term t is transformed into 2t + 3, the difference between two transformed consecutive terms is (2(t + 5) + 3) − (2t + 3) = 10. The multiplication by 2 scales the common difference from 5 to 10. Adding the same constant 3 to every term shifts the entire sequence but does not change the difference between terms, because the two +3 terms cancel. Therefore the new common difference is 10, so option C is correct.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
The original sequence is an arithmetic progression because consecutive terms differ by 11 − 6 = 5 and 16 − 11 = 5. If each original term t is transformed into 2t + 3, the difference between two transformed consecutive terms is (2(t + 5) + 3) − (2t + 3) = 10. The multiplication by 2 scales the common difference from 5 to 10. Adding the same constant 3 to every term shifts the entire sequence but does not change the difference between terms, because the two +3 terms cancel. Therefore the new common difference is 10, so option C is correct.
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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