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  • Let the first term a and the common ratio r of a geometric progression be positive integers. If the sum of squares of its first three is 33033, then the sum of these terms is equal to :<div cla

Let the first term a and the common ratio r of a geometric progression be positive integers. If the sum of squares of its first three is 33033, then the sum of these terms is equal to :

Option: 1

210


Option: 2

220


Option: 3

231


Option: 4

241


Answers (1)

best_answer

Let  a, ar , ar^{2} be three terms of GP

Given : \mathrm{a}^2+(a r)^2+\left(\mathrm{ar}^2\right)^2=33033

\begin{aligned} & a^2\left(1+r^2+r^4\right)=11^2 \cdot 3.7 .13 \\ & \Rightarrow \mathrm{a}=11 \text { and } 1+r^2+r^4=3.7 .13 \\ & \Rightarrow r^2\left(1+r^2\right)=273-1 \\ & \Rightarrow r^2\left(r^2+1\right)=272=16 \times 17 \\ & \Rightarrow r^2=16 \\ & \therefore r=4 \quad \quad[\because r>0] \end{aligned}

Sum of three terms   =a+ar+ar^{2}+a=(1+r+r^{2})

=11(1+4+16)\ 

=11\times21=231

 

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