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

Question

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

Smart Achievers · Accepted Answer

(9525)

$The given A.P. is 3, 8, 13, \dots, 373$

$T_{n} = a + (n - 1) d \Rightarrow 373 = 3 + (n - 1) 5 \Rightarrow n = 75$

$S_{n} = \frac{75}{2} [3 + 373] = 14100$

$Numbers which are divisible by 3 are 3, 18, \dots, 363$

$T_{n'} = 3 + (n' - 1) 15$

$\Rightarrow 363 = 3 + 15 n' - 15 \Rightarrow 15 n' = 375 \Rightarrow n' = 25$

$S_{n'} = \frac{25}{2} [3 + 363] = 4575$

$∴$ $Required sum = 14100 - 4575 = 9525$

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