In the AP (-68,-49,-30,\ldots), what is the first term greater than (700)?
Answer and explanation
Correct answer: 711
Here, the first term is \(a=-68\) and the common difference is \(d=19\). Thus, \(a_n=-68+19(n-1)\). For \(a_n>700\), \(-68+19(n-1)>700\), giving \(n>41.42\). The smallest integer value is \(n=42\). Therefore, \(a_{42}=711\), so 711 is the first term greater than 700. Although 692 is the nearest preceding term, it is less than 700. Exam tip: for the “first term greater than” condition, solve the inequality and take the smallest valid integer \(n\).
Frequently asked questions
What is the correct answer to this question?
711
Why is this the correct answer?
Here, the first term is \(a=-68\) and the common difference is \(d=19\). Thus, \(a_n=-68+19(n-1)\). For \(a_n>700\), \(-68+19(n-1)>700\), giving \(n>41.42\). The smallest integer value is \(n=42\). Therefore, \(a_{42}=711\), so 711 is the first term greater than 700. Although 692 is the nearest preceding term, it is less than 700. Exam tip: for the “first term greater than” condition, solve the inequality and take the smallest valid integer \(n\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the $n$th term of an AP.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
