Class XI Chapter 9 – Sequences and Series Maths ______________________________________________________________________________ 120 2 n 3 1 3 n 3 1 80 n 3 81 n 3 3 n 4 4 Thus, four terms of the given G.P. are required to obtain the sum as 120. Question 14: The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to n terms of the G.P. Solution 14: Let the G.P. be a ar ar 2 3 , , , ar ,.... 2 3 4 5 a ar ar 16 and ar ar ar 128 2 1 16 ...... 1 a r r 3 2 ar 1 r r 128 ...... 2 Dividing equation (2) by (1), we obtain 3 3 ar 1r r 128 2 a 1r r 16 3 r r 2 8 Substituting a 7 16 a S n 16 7 r 2 in (1), we obtain n a r 1 r 1 n 16 2 1 16 2 n S n 1 7 2 1 7 According to the given condition, a 1 2 4 16 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 15: Given a G.P. with Solution 15: a729 a 64 7 a 729 and 7 th term 64, determine Let r be the common ratio of the G.P. It is known that, an a r n 1 a7 ar 729 r 64 729r r 3 7 1 6 6 2 2 r 3 Also, it is known that, S n S 6 a 1 r 1 r 7 n 6 7 2 729 1 3 2 1 3 7 2 3 729 1 3 3 2 7 3 7 7 7 3 7 7 3 2 2187 128 2059 S 7 . Question 16: Find a G.P. for which sum of the first two terms is Solution 16: Let a be the first term and r be the common ratio of the G.P. According to the given conditions, 4and the fifth term is 4 times the third term. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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