Muft Shiksha
Update

Muft Shiksha™ एक 100% Free Education Portal है 🇮🇳, जिसका उद्देश्य Class 9–12 के हर विद्यार्थी तक High-Quality Education को पूरी तरह मुफ्त पहुँचाना है। 🇮🇳 हम मानते हैं कि अच्छी शिक्षा किसी student की आर्थिक स्थिति पर निर्भर नहीं होनी चाहिए। 🇮🇳 हर विद्यार्थी को वही Quality Study Material, MCQs, Quizzes, Exam Preparation, Concept-Based Learning और Bilingual Support मिलना चाहिए, जो आमतौर पर महंगी Coaching या Premium Platforms में मिलता है। Muft Shiksha™ 🇮🇳 इसी सोच के साथ बनाया गया है

Subjects
Class 10MathematicsArithmetic Progressions (AP)Finding the $n$th term of an APExpertLevel 66

In an AP, p, q and r are positive integers such that \(q-p=r-q\). Which relation among these terms is always true?

Advertisement

Answer and explanation

Correct answer: \(a_p+a_r=2a_q\)

For an AP, \(a_k=a_1+(k-1)d\). As \(q-p=r-q\), we get \(p+r=2q\), so \(a_p+a_r=2a_q\). The product relation is associated with a GP, not an AP. Exam tip: equally spaced indices make the middle term the average.

Tags

arithmetic progressionnth termap propertiesindexed termsalgebraic reasoning

Frequently asked questions

What is the correct answer to this question?

\(a_p+a_r=2a_q\)

Why is this the correct answer?

For an AP, \(a_k=a_1+(k-1)d\). As \(q-p=r-q\), we get \(p+r=2q\), so \(a_p+a_r=2a_q\). The product relation is associated with a GP, not an AP. Exam tip: equally spaced indices make the middle term the average.

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.

Report question
Advertisement