Question
Download Solution PDFएक समांतर श्रेणी जिसका पहला और तीसरा पद क्रमशः 160 और 170 है, इसके पहले 157 पदों का योगफल ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
प्रथम पद (a) = 160
तृतीय पद = 170
कुल पद (n) = 157
प्रयुक्त सूत्र:
एक समांतर श्रेणी के प्रथम n पदों का योग (Sn) = n/2 × [2a + (n - 1) × d]
सर्वान्तर (d) = (तृतीय पद - प्रथम पद) / (3 - 1)
गणना:
d = (170 - 160) / 2
⇒ d = 10 / 2
⇒ d = 5
S157 = 157/2 × [2 × 160 + (157 - 1) × 5]
⇒ S157 = 157/2 × [320 + 156 × 5]
⇒ S157 = 157/2 × [320 + 780]
⇒ S157 = 157/2 × 1100
⇒ S157 = 157 × 550
⇒ S157 = 86350
प्रथम 157 पदों का योग 86350 है।
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