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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?
(b) $\sqrt{3}, 3, 3\sqrt{3}, …$ is 729?
(c) $\frac{1}{3}, \frac{1}{9}, \frac{1}{27}, …$ is $\frac{1}{19683}$ ?

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