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Question

If the second and fifth terms of a $$GP$$ are $$24$$ and $$3$$ respectively, then the sum of first six terms is


A
181
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B
1812
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C
189
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D
1892
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E
191
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Solution

The correct option is D $$\dfrac{189}{2}$$
Let $$a$$ be first term and $$r$$ be common ratio.
$$t_2=ar=24$$ and $$t_5=ar^4=3$$
$$\cfrac{t_5}{t_2}=\cfrac{ar^4}{ar}=\cfrac{3}{24}$$
$$\Rightarrow r^3=\cfrac18$$
$$\Rightarrow r=\cfrac12$$
and $$a\times \cfrac12=24\Rightarrow a=48$$
Now, $$S_6=\cfrac{a(1-r^6)}{1-r}=\cfrac{48(1-\cfrac1{64})}{1-\cfrac12}=\cfrac{48\times63\times2}{64}=\cfrac{189}2$$
Hence, D is the correct option.

Mathematics

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