Question
Download Solution PDFयदि अनुक्रम a, a - b, a - 2b, a - 3b,. . का 10वाँ पद 20 है और 20वाँ पद 10 है, तो श्रेणी का xवाँ पद कौन-सा है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया:
अनुक्रम a, a - b, a - 2b, a - 3b,......का 10वाँ पद 20 है। 20वाँ पद 10 है।
गणना:
10वाँ पद = a - 9b = 20 --(1)
20वाँ पद = a - 19b = 10 ---(2)
समीकरण (2) को (1) से घटाने पर:
a - 9b - (a - 19b) = 20 - 10
⇒ a - 9b - a + 19b = 10
⇒ 10b = 10
⇒ b = 1
समीकरण (1) से:
a - 9 (1) = 20
⇒ a = 20 + 9 = 29
अब, xवां पद = a - (x - 1)b
⇒ 29 - (x - 1) (1)
⇒ 29 - x + 1 = 30 - x
∴ अनुक्रम का xवाँ पद 30 - x है ।
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