If a_n = 5n + (−1)^n, what will be the value of a_10 − a_9?
Answer and explanation
Correct answer: 7
The governing concept is evaluation of an explicit sequence rule containing an alternating-sign term. Substitute n = 10 and n = 9 separately. Since 10 is even, (−1)^10 = 1, so a_10 = 5(10) + 1 = 51. Since 9 is odd, (−1)^9 = −1, so a_9 = 5(9) − 1 = 44. Therefore, a_10 − a_9 = 51 − 44 = 7, making option C correct. The alternating term cannot be treated as having the same sign for both indices. Option A would result from ignoring the change in sign, while options B and D reflect arithmetic or subtraction errors. Evaluating each term independently avoids these mistakes.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
The governing concept is evaluation of an explicit sequence rule containing an alternating-sign term. Substitute n = 10 and n = 9 separately. Since 10 is even, (−1)^10 = 1, so a_10 = 5(10) + 1 = 51. Since 9 is odd, (−1)^9 = −1, so a_9 = 5(9) − 1 = 44. Therefore, a_10 − a_9 = 51 − 44 = 7, making option C correct. The alternating term cannot be treated as having the same sign for both indices. Option A would result from ignoring the change in sign, while options B and D reflect arithmetic or subtraction errors. Evaluating each term independently avoids these mistakes.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Explicit or general rule.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
