# Lecture - 7 Chapter 9 Sequences & Series

 NCERT EXERCISE 9.3

Question 19. Find the sum of the products of the corresponding terms of the sequences 2, 4, 8, 16, 32 and 128, 32, 8, 2, $$\frac{1}{2}$$

Question 20. Show that the products of the corresponding terms of the sequences $$a, ar, ar^2, …, ar^{n-1}$$ and $$A, AR, AR^2,…, AR^{n-1}$$ form a G.P, and find the common ratio.

Question 21. Find four numbers forming a geometric progression in which the third term is greater than the first term by 9, and the second term is greater than the 4th by 18.

Question 22. If pth, qth and rth terms of a G.P. are a, b and c, respectively. Prove that $$a^{q-r}b^{r-p}c^{p-q}=1$$

Question 23. If the first and the nth term of a G.P. are a and b, respectively, and if P is the product of n terms, prove that $$P^2=(ab)^n$$.

Question 24. Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from $$(n+1)^{th} text{ to } (2n)^{th}$$ term is $$\frac{1}{r^n}$$

Question 25. If a, b, c and d are in G.P. show that $$(a^2+b^2+c^2)(b^2+c^2+d^2)=(ab+bc+cd)^2$$.