Q. 24 A5.0( 2 Votes )

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

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

S29 = 5220

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

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