Question

The sum of 11 consecutive natural numbers is 2761,then find the middle number.

Answer 1

(x), (x+1),(x+2)....(x+11)
Sn = 2761 a= x. d=1. n=11

Sn = (n/2) [ 2a + (n-1)d ]
2761 = (11/2) [ 2(x) + (11-1)(1) ]
2761x2 = 11(2x+10)
502= 2x + 10
x= 246
middle term is (x+5) therefore 246+5=251

Answer 2

Middle number = 251 if The sum of 11 consecutive natural numbers is 2761

Step-by-step explanation:

Let say 11 consecutive numbers are

a  , a + 1 , a + 2 , ..................................................., a + 9 , a + 10

This is an AP

Where first term = a

number of term = 11

Last term = a + 10

Sum of 11 Terms = (11/2)(a + a + 10)

= 11(a + 5)

11(a + 5) = 2761

=> a + 5 = 251

Middle term  = (a + a + 10)/2  = a + 5

Hence middle number = 251

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