The sum of all those terms, of the arithmetic progression 3, 8, 13, ...., 373, which are n…

Question

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

Answer: 9525

Accepted Answer

The sum of all those terms, of the arithmetic progression $3,8,13\ldots ,373$.

Which are not divisible by 3 is

$\begin{gathered} =(3+8+13+18+\ldots +373)-(3+18+33+\ldots +363) \ =\frac{75}{2}(3+373)-\frac{25}{2}(3+363) \ =\frac{75}{2}	imes 376-\frac{25}{2}	imes 366 \ =75	imes 188-25	imes 183 \ =14100-4575 \ =9525 \end{gathered}$

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