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In an arithmetic progression (AP), if a₇ + a₁₉ = 156, what is the value of a₁₃?किसी समानांतर श्रेणी (AP) में यदि a₇ + a₁₉ = 156 हो, तो a₁₃ का मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 7878
The term a₁₃ is midway between a₇ and a₁₉ because the indices are equally spaced: 13 − 7 = 19 − 13 = 6. In an AP, the middle term is the average of the two equally spaced terms, so 2a₁₃ = 156 and a₁₃ = 78.a₁₃, a₇ और a₁₉ के बीच का मध्य पद है, क्योंकि सूचकांकों की दूरियाँ बराबर हैं: 13 − 7 = 19 − 13 = 6। समानांतर श्रेणी में ऐसा मध्य पद दोनों पदों का औसत होता है। इसलिए 2a₁₃ = 156 और a₁₃ = 78।
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