Q. 24 A5.0( 2 Votes )

Find the sum of the numbers lying between 107 and 253 that are multiples of 5.

Answer :

The numbers lying between 107 and 253 that are multiples of 5 are


110, 115, 120,…, 250


a2 – a1 = 115 – 110 = 5


a3 – a2 = 120 – 115 = 5


a3 – a2 = a2 – a1 = 5


Therefore, the series is in AP


Here, a = 110, d = 5 and an = 250


We know that,


an = a + (n – 1)d


250 = 110 + (n – 1)5


250 – 110 = (n – 1)5


140 = (n – 1)5


28 = (n – 1)


n = 29


Now, we have to find the sum of this AP




S29 = 29[110 + 14 × 5]


S29 = 29[180]


S29 = 5220


Hence, the sum of all numbers lying between 107 and 253 is 5220.


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