What is the common difference of the sequence (a_n=7-0.5n)?
Answer and explanation
Correct answer: (-0.5)
An arithmetic progression can be written in the form a_n=a_1+(n-1)d, so the coefficient of n in a linear expression for its terms equals the common difference. Here a_n=7-0.5n. Increasing n by 1 changes the term by -0.5: a_{n+1}-a_n=[7-0.5(n+1)]-[7-0.5n]=-0.5. Thus the sequence decreases by one-half at every step, and its common difference is -0.5. Option D is correct. Option B gives the magnitude but misses the negative sign, while options A and C confuse the constant or the coefficient with the required difference.
Frequently asked questions
What is the correct answer to this question?
(-0.5)
Why is this the correct answer?
An arithmetic progression can be written in the form a_n=a_1+(n-1)d, so the coefficient of n in a linear expression for its terms equals the common difference. Here a_n=7-0.5n. Increasing n by 1 changes the term by -0.5: a_{n+1}-a_n=[7-0.5(n+1)]-[7-0.5n]=-0.5. Thus the sequence decreases by one-half at every step, and its common difference is -0.5. Option D is correct. Option B gives the magnitude but misses the negative sign, while options A and C confuse the constant or the coefficient with the required difference.
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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