Class XI Chapter 9 – Sequences and Series Maths ______________________________________________________________________________ 2 1 1 360 1 361 r 10 or 9 2 2 r 3 [Taking real roots] Thus, the common ratio of the G.P. is 3. Question 10: The sum of the three numbers in G.P. is 56. If we subtract 1, 7, 21 from these numbers in that order, we obtain an arithmetic progression. Find the numbers. Solution 10: Let the three numbers in G.P. be a, ar , and From the given condition, a ar ar 2 56 2 1 56 ...... 1 a r r a ar ar 2 1, 7, 21 forms an A.P. ar 7 a 1 ar 2 21 ar 7 ar a ar ar 2 ar ar a 2 6 14 2 8 2 ar ar ar a 2 1 2r 8 2 2 1 8 ...... 2 a r ar 8 From (1) and (2), we get 7 r 2r 1 1 r r 2 2 2 2 7r 14r 7 1 r r 0 2 6r 15r 6 0 2 6r 12r 3r 6 0 6r r 2 3 r 2 0 r r 6 3 2 0 b 2 ar When r 2, a 8 When Therefore, when When, r 1/ 2 , the three numbers in G.P. are 32, 16 and 8. Thus, in either case, the three required numbers are 8, 16 and 32. r 2, the three numbers in G.P. are 8, 16 and 32. . 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 **11**: A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio. Solution **11**: Let the G.P. be T1 , T2 , T3 , T4.... T 2n . 2n Number of terms According to the given condition, T T T .... T 5 T T .... T 1 2 3 2n 1 3 2n 1 T1 T2 T3 .... T2 n 5 T1 T3 ..... T2 n 1 0 T T .... T 4 T T ..... T 2 4 2n 1 3 2n 1 Let the G.P. be a ar ar 2 3 , , , ar ... n n 1 4 ar 1 ar r r1 r1 ar 4a r 4 Thus, the common ratio of the G.P. is 4. Question 12: The sum of the first four terms of an A.P. is 56. The sum of the last four terms is **11**2. If its first term is **11**, then find the number of terms. Solution 12: Let the A.P. be Sum of first four terms Sum of last four terms a, a d, a 2 d, a 3 d.... a n 2 d, a n 1 d. a a d a 2d a 3d 4a 6d 4 3 2 1 a n d a n d a n d a n d 4a 4n 10 d According to the given condition, 4a6d 56 4**11** 6d 56 [Since **11**given 6d 12 d 2 4a 4n 10 d **11**2 a ] Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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