Last updated at March 19, 2021 by Teachoo
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Ex 5.3, 1 Find the sum of the following APs. (i) 2, 7, 12 ,โฆ., to 10 terms. 2, 7, 12,โฆ., to 10 term s We know that Sum of AP = ๐/2 (2a + (n โ 1) d) Here n = 10, a = 2, & d = 7 โ 2 = 2 Putting these in formula , Sum = ๐/๐ (2a + (n โ 1) d) = 10/2 (2 ร 2 + (10 โ 1) ร 5) = 5(3 + 9 ร 5) = 5 (4 + 45) = 5 (49) = 245 Ex 5.3, 1 Find the sum of the following APs. (ii) โ37, โ33, โ29 ,โฆ, to 12 terms โ37, โ33, โ29 ,โฆ, to 12 terms We know that Sum = ๐/2 (2a + (n โ 1)d) Here n = 12, a = โ37 & d = โ 33 โ (โ37) = โ 33 + 37 = 4 Putting values in formula Sum = ๐/๐ (2a + (n โ 1) d) = 12/2 (2 ร (โ37) + (12 โ 1) ร 4) = 6 (โ74 + 11 ร 4) = 6 (โ74 + 44) = 6 (โ30) = โ180 Ex 5.3, 1 Find the sum of the following APs. (iii) 0.6, 1.7, 2.8 ,โฆโฆ.., to 100 terms 0.6, 1.7, 2.8,โฆโฆ to 100 terms We know that Sum = ๐/2 (2a + (n โ 1) d) Here n = 100, a = 0.6, & d = 1.7 โ 0.6 = 1.1 Putting in formula Sum = ๐/๐ (2a + (n โ 1) d) = 100/2 (2 ร 0.6 + (100 โ 1) ร 1.1) = 50(1.2 + 99 ร 1.1) = 50(1.2 + 108.9) = 50 (110.1) = 50 ร 110 . 1 = 5505 Ex 5.3, 1 Find the sum of the following APs. (iv) 1/15, 1/12, 1/10 ,โฆโฆโฆ, to 11 terms 1/15, 1/12, 1/10, โฆ.. to 11 terms We know that Sum = ๐/2 (2a + (n โ 1) d) Here n = 11 , a = 1/15 & d = 1/12 โ 1/15 = (15 โ 12)/(12 ร 15) = 3/180 = 1/60 Putting values in formula Sum = ๐/๐ (2a + (n โ 1) d) = 11/2 ("2 " ร" " 1/15 " + (11 โ 1) " ร" " 1/60) = 11/2 (2/15 " + 10 " ร 1/60) = 11/2 (2/15 " + " 10/60) = 11/2 ((2 ร 4 + 10)/60) = 11/2 ((8 + 10)/60) = 11/2 ร 18/60 = 11 ร 9/60 = 11 ร 3/20 = ๐๐/๐๐
Ex 5.3
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