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समांतर श्रेणी

Question
CBSEHHIMAH10010195

निम्नलिखित समांतर श्रेढियों का योग ज्ञात कीजिए:
0.6, 1.7, 2.8, ... 100 पदों तक

Solution

यहाँ, a = 0.6
d = 1.7 – 0.6 = 1.1, n = 100
straight S subscript straight n space equals space straight n over 2 space left square bracket space 2 straight a space plus space left parenthesis straight n space minus space 1 right parenthesis space straight d space right square bracket
therefore space straight S subscript 100 space equals space 100 over 2 space left square bracket space 2 space cross times space 0.6 space plus space left parenthesis 100 space minus space 1 right parenthesis space cross times space 1.1 space right square bracket
= 50 x [ 2 x 0.6 + (100 - 1) x 1.1 ]
= 50 x [ 1.2 + 108.9 ]
= 50 x 110.1 = 5505.0
अत: दी गई A.P. के प्रथम 100 पदों का योगफल = 5505