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  • The sum of all those terms, of the arithmetic progression 3, 8, 13, ...., 373, which are not divisible by 3, is equal to _____.Option: 1 9525<

The sum of all those terms, of the arithmetic progression 3, 8, 13, ...., 373, which are not divisible by 3, is
equal to _____.

Option: 1

9525


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\begin{aligned} & \text { A.P : } 3,8,13 \ldots .373 \\ & T_n=a+(n-1) d \\ & 373=3+(n-1) 5 \\ & \Rightarrow \mathrm{n}=\frac{370}{5} \\ & \Rightarrow n=75 \end{aligned}

$$ \begin{aligned} & \text { Now Sum }=\frac{\mathrm{n}}{2}[\mathrm{a}+1] \\ & =\frac{75}{2}[3+373]=14100 \end{aligned}

Now numbers divisible by 3 are

\begin{aligned} & 3,18,33 \ldots \ldots .363 \\ & 363=3+(\mathrm{k}-1) 15 \\ & \Rightarrow \mathrm{k}-1=\frac{360}{15}=24 \Rightarrow \mathrm{k}=25 \\ & \text { Now, sum }=\frac{25}{2}(3+363)=4575 \mathrm{~s} \\ & \therefore \text { req. sum }=14100-4575 \\ & =9525 \end{aligned}

Posted by

vishal kumar

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