L5 Class 11 Maths Sequences and Series

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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 20th and nth terms of the G.P. \frac{5}{2}, \frac{5}{4}, \frac{5}{8}, …

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

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

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

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