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


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)