AP Police Constable previous year question

If the sum of the first n terms of an arithmetic progression is 7n 2 + 2n, then the sum of its third and fifth terms is:

Asked in AP Police Constable Prelims: 2016 (06 Nov 2016) · Quantitative Aptitude

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Correct answer: (C) 102

Given: Sum of first ‘n’ terms = 7n 2+ 2n Formula: Sum of ‘n’ terms of an AP = n/2 × [2a + (n – 1)d] [a = first term, d = common difference] nth term = a + (n – 1)d Calculation: Sum of 5 terms, (n = 5) 5/2 × [2a + 4d] = 7 × (5) 2+ 2 × 5 ⇒ a + 2d = 35 + 2 = 37 ----(i) Sum of 4 terms, (n = 4) 4/2 × (2a + 3d) = 7 × (4) 2+ 2 × 4 ⇒ 2a + 3d = 7 × 8 + 4 = 60 ----(ii) From (i) and (ii), we get a = 9, d = 14 3 rd term = a + 2d = 37 5 th term = a + 4d = 65 ∴ Required sum = 37 + 65 = 102

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ఒక అంకగణిత శ్రేఢి యొక్క మొదటి n పదాల మొత్తం 7n² + 2n అయితే, దాని మూడవ మరియు ఐదవ పదాల మొత్తం:

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सही उत्तर: (C) 102

दिया गया है: प्रथम 'n' पदों का योग = 7n²+2n सूत्र: समांतर श्रेढ़ी (AP) के 'n' पदों का योग = n/2 × [2a + (n – 1)d] [a = प्रथम पद, d = सार्व अंतर] nवां पद = a + (n – 1)d गणना: 5 पदों का योग (n = 5) 5/2 × [2a + 4d] = 7 × (5)² + 2 × 5 ⇒ a + 2d = 35 + 2 = 37 ----(i) 4 पदों का योग (n = 4) 4/2 × (2a + 3d) = 7 × (4)² + 2 × 4 ⇒ 2a + 3d = 7 × 8 + 4 = 60 ----(ii) (i) और (ii) से, a = 9, d = 14 3रा पद = a + 2d = 37 5वां पद = a + 4d = 65 ∴ अभीष्ट योग = 37 + 65 = 102

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If the sum of the first n terms of an arithmetic progression is 7n 2 + 2n, then the sum of its third and fifth terms is:

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