## Class 11 Maths Chapter 9 Lecture 13

“Leaders Are Anticipatory Thinkers. They Consider All Consequences Of Their Behaviors Before They Act.”

# Lecture - 13 Chapter 9 Sequences & Series

 MISCELLANEOUS EXERCISE

Question 18. If a and b are the roots of $$x^2-3x+p=0$$ and cd are roots of $$x^2-12x+q=0$$, where abcd form a G.P. Prove that $$(q+p):(q-p)=17:15$$.

Question 19. The ratio of the A.M. and G.M. of two positive numbers a and b, is m : n. Show that $$a:b = (m+\sqrt{m^2-n^2}):(m-\sqrt{m^2-n^2})$$.

Question 20. If a, b, c are in A.P.; b, c, d are in G.P. and $$\frac{1}{c}, \frac{1}{d}, \frac{1}{e}$$ are in A.P. prove that ac, e are in G.P.

Question 21. Find the sum of the following series up to n terms:
(i) 5 + 55 +555 + …
(ii) .6 +. 66 +. 666+…

Question 22. Find the 20th term of the series 2 × 4 + 4 × 6 + 6 × 8 + … + n terms.

Question 23. Find the sum of the first n terms of the series: 3+ 7 +13 +21 +31 +…

Question 24. If $$S_1, S_2, S_3$$ are the sum of first n natural numbers, their squares and their cubes, respectively, show that $$9{S_2}^2=S_3(1+8S_1)$$.