In an AP, (a_p=29), (a_{p+10}=99), and (p=8). What is (a_{35})?
Answer and explanation
Correct answer: 218
Since p=8, a_p=a_8=29 and a_{p+10}=a_{18}=99. The difference over 10 terms is 99-29=70, so the common difference is d=70/10=7. Therefore, a_{35}=a_8+(35-8)d=29+27×7=218. Choosing 225 would incorrectly require a difference of 28 terms instead of 27 from the 8th term. Exam tip: when finding d from two terms, always use the difference between their indices.
Frequently asked questions
What is the correct answer to this question?
218
Why is this the correct answer?
Since p=8, a_p=a_8=29 and a_{p+10}=a_{18}=99. The difference over 10 terms is 99-29=70, so the common difference is d=70/10=7. Therefore, a_{35}=a_8+(35-8)d=29+27×7=218. Choosing 225 would incorrectly require a difference of 28 terms instead of 27 from the 8th term. Exam tip: when finding d from two terms, always use the difference between their indices.
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.
