Ex 5.3, 2 - Chapter 5 Class 10 Arithmetic Progressions

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Ex 5.3, 2 Find the sums given below (i) 7 + 101/2 + 14 + ………… + 84 7 + 10 1/2+14+…84 Here, a = 7 d = 10 1/2−7 = 21/2−7 = (21 − 14)/2 = 7/2 Also, last term = 𝒍 = 84 To find sum, first we need to find n Using formula an = a + (n − 1)d Putting a = 7, d = 7/2, an = 84 in the formula 84 = 7 + (n − 1) × 𝟕/𝟐 84 − 7 = (n − 1) × 7/2 77 = (n − 1) × 7/2 77 × 2/7 = (n − 1) 22 = n − 1 n = 22 + 1 n = 23 For sum, we use the formula S = 𝒏/𝟐 (𝒂+𝒍) Putting a = 7, n = 23, l = 84 S = 23/2(7+84) S = 23/2×91 S = 2093/2 S = 1046.5 Ex 5.3, 2 Find the sums given below (ii) 34 + 32 + 30 + ……….. + 10 34 + 32 + 30 + ……….. + 10 Here, a = 34 d = 32 – 34 = –2 Also, Last term = 𝒍 = 10 To find sum, first we need to find n Using formula an = a + (n − 1)d Putting a = 34, d = −2, an = 10 in the formula 10 = 34 + (n − 1) × −2 10 − 34 = (n − 1) × −2 −24 = (n − 1) × −2 (−24)/(−2) = (n − 1) 12 = n − 1 n = 12 + 1 n = 13 For sum, we use the formula S = 𝒏/𝟐 (𝒂+𝒍) Putting a = 34, n = 13, l = 10 S13 = 13/2 (34+10) S13 = 13/2 (44) S13 = 286 Ex 5.3, 2 Find the sums given below (iii) − 5 + (−8) + (−11) + ………… + (−230) − 5 + (−8) + (−11) + ………… + (−230) Here, a = –5 d = –8 – (–5) = –8 + 5 = –3 Also, Last term = 𝒍 = –230 To find sum, first we need to find n Using formula an = a + (n − 1)d Putting a = −5, d = −3, an = −230 in the formula −230 = −5 + (n − 1) × −3 −230 + 5 = (n − 1) × −3 −225 = (n − 1) × −3 (−225)/(−3) = (n − 1) 75 = n − 1 n = 75 + 1 n = 76 For sum, we use the formula S = 𝒏/𝟐 (𝒂+𝒍) Putting a = −5, n = 76, l = −230 Sn = 76/2 (−5 + (−230)) Sn = 38 (– 235) Sn = –8930