**Question 6:**The first three terms of a sequence are 2,

*x*, 18. Find the positive value of

*x*so that the sequence is

(a) an arithmetic progression,

(b) a geometric progression.

*Solution*:

**Question 7:**Given a geometric progression $\frac{2}{z},\text{}3,\text{}\frac{9z}{2},\text{}q,\mathrm{\dots .}$ express

*q*in terms of

*z*.

*Solution*:

**Question 8:**The second and the fourth term of a geometry progression are 10 and $\frac{2}{5}$ respectively. Find

(a) The first term and the common ratio where r > 0,

(b) The sum to infinity of the geometry progression.

*Solution*:

**Question 9:**In a geometric progression, the first term is 18 and the common ratio is

*r*.

Given that the sum to infinity of this progression is 21.6, find the value of

*r*.

*Solution*:

**Question 10:**In a geometric progression, the first term is 27 and the fourth term is 1. Calculate

(a) the positive value of common ratio,

*r*,

(b) the sum of the first

*n*terms where

*n*is sufficiently large till ${r}^{n}\approx 0$

*Solution*:
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