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
B
1812
C
189
D
1892
E
191

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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