SATHEE: Sequences and Series 3 Question 7

Sequences and Series 3 Question 7

7.

If the $2$ nd, $5$ th and $9$ th terms of a non-constant $A P$ are in GP, then the common ratio of this GP is

(2016 Main)

(a) $\frac{8}{5}$

(b) $\frac{4}{3}$

(d) $\frac{7}{4}$

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Answer:

Correct Answer: 7. (b)

Solution:

Let $a$ be the first term and $d$ be the common difference.

Then, we have $a + d, a + 4 d, a + 8 d$ in GP,

i.e. $(a + 4 d)^{2} = (a + d) (a + 8 d)$

$\Rightarrow a^{2} + 16 d^{2} + 8 a d = a^{2} + 8 a d + a d + 8 d^{2}$

$\Rightarrow 8 d^{2} = a d$

$\Rightarrow 8 d = a$

$[∵ d \neq 0]$

Now, common ratio,

$r = \frac{a + 4 d}{a + d} = \frac{8 d + 4 d}{8 d + d} = \frac{12 d}{9 d} = \frac{4}{3}$

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Sequences and Series 3 Question 7

7.

Answer:

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