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Q.

The sum of the numbers lying between 107 and 253 that are multiples of 5 is ____.

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Detailed Solution

The sum of the numbers lying between 107 and 253 that are multiples of 5 is 5220.
We need to find the sum of the numbers lying between 107 and 253 that are multiples of 5.
The numbers between 107 and 253 which are divisible by 5 are 110, 115, 120,.......250 which is an A.P. as the common difference is same.
We know,
The sum of the n terms of the A.P. is

S u m = n 2 2 a + n − 1 d

The formula for

n^{th}

term of the A.P. is

T n = a + n − 1 d

where,
The first term is a.
The common difference is d.
The number of terms are n.
Substituting the values of a,n,d in the formula of

n^{th}

term,

T n = a + n − 1 d ⇒ 250 = 110 + n − 1 5 ⇒ 250 − 110 = 5 n − 5 ⇒ 140 = 5 n − 5

So, the value of n is ,

140 = 5 n − 5 ⇒ 5 n = 140 + 5 ⇒ 5 n = 145 ⇒ n = 29

Therefore,

Sum = n 2 2 a + n − 1 d ⇒ Sum = 292 2 × 110 + 29 − 1 5 ⇒ Sum = 292 220 + 140 ⇒ Sum = 292 × 360 ⇒ Sum = 29 × 180 ⇒ Sum = 5220

The sum of the series between 107 and 253 that are multiple of 5 is 5220.

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