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# 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 4^{th} by 18.

**Question 22.** If *p*^{th}, *q*^{th} and *r*^{th} 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 *n*^{th} 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 \((a^2+b^2+c^2)(b^2+c^2+d^2)=(ab+bc+cd)^2\).