Question 1 and 2, Exercise 4.4

Solutions of Question 1 and 2 of Exercise 4.4 of Unit 04: Sequence and Series. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan.

Determine whether each sequence is geometric. If so, find the common ratio. $5,20,100,500, \ldots$

Solution.

Given sequence is $5, 20, 100, 500, \ldots $.
A sequence is geometric if any two of its consecutive terms have same ratio. Here \begin{align*} \frac{20}{5} = 4\neq \frac{100}{20} = 5.\end{align*} Hence given sequence is not geometric. GOOD

Alternative Method

Given sequence is $5, 20, 100, 500, \ldots $.
Suppose \begin{align*} r_1& =\frac{20}{5} = 4\\ r_2&=\frac{100}{20} = 5\\ r_3&=\frac{500}{100} = 5. \end{align*} Since $r_1 \neq r_2$, it means two consective terms has different ratio.
Hence given sequence is not geometric. GOOD

Determine whether each sequence is geometric. If so, find the common ratio. $2,4,6,8, \ldots$

Solution.

Given sequence is \(2, 4, 6, 8, \ldots\).
Suppose \begin{align*} r_1&=\frac{4}{2} = 2 \\ r_2&=\frac{6}{4} = \frac{3}{2} \\ r_3&=\frac{8}{6} =\frac{4}{3} \end{align*} Since $r_1 \neq r_2 \neq r_3$, it means two consecutive terms has different ratio.
Hence given sequence is not geometric. GOOD

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