Class XI Chapter 9 – Sequences and Series Maths ______________________________________________________________________________ 2 n n1 3n 3n 8n 4 6 2 6 2 n n 1 3 n **11** n 10 12 2 n n1 3 n 6 n 5 n 10 12 n n 1 3 nn 2 5 n 2 12 1 23 5 n n n n 12 Also, n K 1 K 3 2 ...... 2 1 2 12 1 2 n n n n n K 4 6 n n 1 n n 1 2n 1 2 2 3 2 n n1 3n 3n 4n 2 2 6 2 n n 1 3 n 7 n 2 12 2 n n1 3 n 6 n n 2 12 n n1 3 n n 2 1 n 2 12 1 23 1 n n n n 12 From (1), (2) and (3), we obtain ...... 3 1 23 5 2 2 2 12 23 ..... n n1 12 2 2 2 1 2 2 3 .... n n1 n n 1 n 2 3n 5 3n 5 n n 1 n 2 3n 1 3n 1 Thus, the given result is proved. n n n n 1 23 1 n n n n 12 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 9 – Sequences and Series Maths ______________________________________________________________________________ Question 27: A farmer buys a used tractor for Rs. 12000. He pays Rs. 6000 cash and agrees to pay the balance in annual installments of Rs. 500 plus 12% interest on the unpaid amount. How much will be the tractor cost him? Solution 27: It is given farmer pays Rs. 6000 in cash. Therefore, unpaid amount = Rs. 12000 – Rs. 6000 = Rs. 6000 According to the given condition, the interest paid annually is 12% of 6000, 12% of 5500, 12% of 5000 ….. 12% of 500 Thus, total interest to be paid = 12% of 6000 + 12% of 5500 + 12% of 5000 + ….. + 12% of 500 = 12% of (6000 + 5500 + 5000 + …. + 500) = 12% of (500 + 1000 + 1500 + ….. + 6000) Now, the series 500, 1000, 1500 …. 6000 is an A.P. with both the first term and common difference equal to 500. Let the number of terms of the A.P. be n . 6000 500 n 1 500 1 n 1 12 n 12 Sum of the A.P 12 2 500 12 1 500 6 1000 5500 6 6500 39000 2 Thus, total interest to be paid = 12% of (500 + 1000 + 1500 + ….. + 6000) = 12% of 39000 = Rs. 4680 Thus, cost of tractor = (Rs. 12000 + Rs. 4680) = Rs. 16680. Question 28: Shamshad Ali buys a scooter for Rs. 22000. He pys Rs. 4000 cash and agrees to pay the balance in annual installment of Rs. 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him? Solution 28: It is given that Shamshad Ali buys a scooter for Rs. 22000 and pays Rs. 4000 in cash. Unpaid amount = Rs. 22000 – Rs. 4000 = Rs. 18000 According to the given condition, the interest paid annually is 10% of 18000, 10% of 17000, 10% of 16000 ….. 10% of 1000 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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**Magazine:** CLASS_11_MATHS_SOLUTIONS_NCERT

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