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# Lecture - 6 Chapter 9 Sequences & Series

NCERT EXERCISE 9.3 |

**Question 11.** Evaluate \( \sum_{k=1}^{11} (2+3^k)\)

**Question 12.** The sum of first three terms of a G.P. is \(\frac{39}{10}\) and their product is 1. Find the common ratio and the terms.

**Question 13.** How many terms of G.P. \( 3, 3^2, 3^3, …\) are needed to give the sum 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.

**Question 15.** Given a G.P. with a = 729 and 7^{th} term 64, determine \( S_7\).

**Question 16.** Find a G.P. for which sum of the first two terms is – 4 and the fifth term is 4 times the third term.

**Question 17.** If the 4^{th}, 10^{th} and 16^{th} terms of a G.P. are *x*, *y* and *z*, respectively. Prove that *x*, *y*, *z* are in G.P.

**Question 18.** Find the sum to n terms of the sequence, 8, 88, 888, 8888… .