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

Step-by-step solution

Given sequence is 3 , 8 , 13 , . . . . . 373 . Here a = 3 ,   d = 5   and   a n = 373 Now a n = a + n - 1 d ⇒ 373 = 3 + n - 1 5 ⇒ n = 75 We know that S n = n 2 a + a n ⇒ S 75 = 75 2 3 + 373 ⇒ S 75 = 14100 Now let us write the sequence of terms which are divisible by 3 . We get, 3 , 18 , 33 , . . . . . 363 ⇒ 363 = 3 + n - 1 15 ⇒ n = 25 Now let us find the sum of terms divisible by 3 . ⇒ S d i v   b y   3 = 25 2 3 + 363 = 4575 Required sum = Sum of 75