If terms are defined by A_n=4n−9, what does A_15−A_14 represent?
Answer and explanation
Correct answer: Common difference
First calculate the two consecutive terms from the given rule. A_15=4(15)−9=60−9=51, while A_14=4(14)−9=56−9=47. Hence A_15−A_14=51−47=4. More generally, substituting n+1 and n gives A_{n+1}−A_n=[4(n+1)−9]−[4n−9]=4, a constant independent of n. The difference between consecutive terms of an arithmetic progression is its common difference, so option B is correct. It is not the first term, the number of terms, or a last term.
Frequently asked questions
What is the correct answer to this question?
Common difference
Why is this the correct answer?
First calculate the two consecutive terms from the given rule. A_15=4(15)−9=60−9=51, while A_14=4(14)−9=56−9=47. Hence A_15−A_14=51−47=4. More generally, substituting n+1 and n gives A_{n+1}−A_n=[4(n+1)−9]−[4n−9]=4, a constant independent of n. The difference between consecutive terms of an arithmetic progression is its common difference, so option B is correct. It is not the first term, the number of terms, or a last term.
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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