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# Lecture - 5 Chapter 9 Sequences & Series

Meaning of Geometric Progression (GP) and its common ratio, General Term of Geometric Progression (nth term of GP), Derivation for Sum to n terms of a GP, Geometric Mean and its relationship with Geometric Progression, Rules Comparison of Arithmetic Progression and Geometric Progression

NCERT EXERCISE 9.3 |

**Question 1.** Find the 20^{th} and *n*^{th} terms of the G.P. \( \frac{5}{2}, \frac{5}{4}, \frac{5}{8}, …\)

**Question 2.** Find the 12^{th} term of a G.P. whose 8^{th} term is 192 and the common ratio is 2.

**Question 3.** The 5^{th}, 8^{th} and 11^{th} terms of a G.P. are *p*, *q* and *s*, respectively. Show that \( q^2=ps\).

**Question 4.** The 4^{th} term of a G.P. is square of its second term, and the first term is – 3. Determine its 7^{th} term.

**Question 5.** Which term of the following sequences:* (a) *\( 2, 2\sqrt{2}, 4, …\) is 128?

*\( \sqrt{3}, 3, 3\sqrt{3}, …\) is 729?*

**(b)***\(\frac{1}{3}, \frac{1}{9}, \frac{1}{27}, …\) is \(\frac{1}{19683}\)?*

**(c)****Question 6.** For what values of *x*, the numbers \( -\frac{2}{7}, x, -\frac{7}{2}\) are in G.P.?

Find the sum to indicated number of terms in each of the geometric progressions in Exercises 7 to 10:

**Question 7.** 0.15, 0.015, 0.0015, … 20 terms.

**Question 8.** \( \sqrt{7}, \sqrt{21}, 3\sqrt{7}, …\) *n* terms.

**Question 9.** \( 1, -a, a^2, -a^3, … n \text{ terms } (\text{ if } a \ne -1)\).

**Question 10.** \( x^3, x^5, x^7, … n \text{ terms} (\text{ if } x \ne \pm 1)\)