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At the end of consecutive hours, the water level in a tank is recorded as 84.5 cm, 81.75 cm, 79.0 cm, ... A student says that the water level at the end of the 16th hour will be \(84.5-16\times2.75=40.5\) cm. Which is the correct analysis of the student's error?एक टंकी में लगातार घंटों के अंत में जल-स्तर क्रमशः 84.5 cm, 81.75 cm, 79.0 cm, ... दर्ज किया गया है। एक छात्र कहता है कि 16वें घंटे का जल-स्तर \(84.5-16\times2.75=40.5\) cm होगा। उसकी त्रुटि का सही विश्लेषण कौन-सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: There are only 15 decreases after the first term; the 16th water level is 43.25 cm.पहले पद के बाद केवल 15 बार कमी होगी; 16वाँ जल-स्तर 43.25 cm होगा।
Here, \(a=84.5\) and \(d=-2.75\). Thus \(a_{16}=a+15d=84.5-15(2.75)=43.25\) cm. The student used 16 instead of \(n-1\). Exam tip: always count the number of jumps from the first term.यहाँ \(a=84.5\) और \(d=-2.75\) है। \(a_{16}=a+15d=84.5-15(2.75)=43.25\) cm। छात्र ने 16 के स्थान पर \(n-1\) नहीं लिया। परीक्षा में पद संख्या से 1 घटाना याद रखें।
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