A sequence has rule (a_n=n^2+n+2). What is (a_5+a_6)?
Answer and explanation
Correct answer: (76)
The governing idea is substitution into an explicit nth-term rule. For n = 5, a₅ = 5² + 5 + 2 = 25 + 5 + 2 = 32. For n = 6, a₆ = 6² + 6 + 2 = 36 + 6 + 2 = 44. Adding the two required terms gives a₅ + a₆ = 32 + 44 = 76, not 78. Therefore option B is correct, so the supplied original key needs correction. A quick algebraic check is (25 + 5 + 2) + (36 + 6 + 2) = 61 + 15 = 76. The other options arise from arithmetic or substitution errors.
Frequently asked questions
What is the correct answer to this question?
(76)
Why is this the correct answer?
The governing idea is substitution into an explicit nth-term rule. For n = 5, a₅ = 5² + 5 + 2 = 25 + 5 + 2 = 32. For n = 6, a₆ = 6² + 6 + 2 = 36 + 6 + 2 = 44. Adding the two required terms gives a₅ + a₆ = 32 + 44 = 76, not 78. Therefore option B is correct, so the supplied original key needs correction. A quick algebraic check is (25 + 5 + 2) + (36 + 6 + 2) = 61 + 15 = 76. The other options arise from arithmetic or substitution errors.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
