एक समांतर श्रेणी जिसका पहला और तीसरा पद क्रमशः 160 और 170 है, इसके पहले 157 पदों का योगफल ज्ञात कीजिए।

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UP Police SI (दरोगा) Official PYP (Held On: 12 Nov 2021 Shift 3)
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  1. 86350
  2. 83350
  3. 84350
  4. 85350

Answer (Detailed Solution Below)

Option 1 : 86350
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यूपी पुलिस SI (दरोगा) सामान्य हिंदी मॉक टेस्ट
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Detailed Solution

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दिया 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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