Question
Download Solution PDFएक समांतर श्रेणी में, तीसरे, चौथे और पाँचवें पदों का योग 12 है। पहले 7 पदों का योग क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
समांतर श्रेणी (AP)
तीसरे, चौथे और पाँचवें पदों का योग = 12
प्रयुक्त सूत्र:
AP का nवाँ पद: an = a + (n - 1)d
AP के पहले n पदों का योग: Sn = (n/2)[2a + (n - 1)d]
जहाँ a पहला पद है और d सार्व अंतर है।
गणना:
तीसरा, चौथा और पाँचवाँ पद:
a3 = a + 2d
a4 = a + 3d
a5 = a + 4d
तीसरे, चौथे और पाँचवें पदों का योग = 12:
(a + 2d) + (a + 3d) + (a + 4d) = 12
3a + 9d = 12
a + 3d = 4 ... (1)
पहले 7 पदों का योग (S7):
S7 = (7/2)[2a + (7 - 1)d]
S7 = (7/2)[2a + 6d]
S7 = 7(a + 3d)
समीकरण (1) से a + 3d = 4 रखने पर:
S7 = 7 x 4
S7 = 28
इसलिए, पहले 7 पदों का योग 28 है।
Last updated on Apr 24, 2025
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