Question

The sum of eleven consecutive integers is 2013. What is the smallest of these integers​

Answer 1

Answer:

Hence last number will be 'a + 10' (Consecutive 11 numbers)

a = -4

Answer 2

Given :

• The sum of eleven consecutive integers is 2013.

To Find :

The smallest of these integers.

Solution :

Let

• First (smallest) integer = x
• Second integer = x + 1
• Third integer = x + 2
• Fourth Integer = x + 3
• Fifth Integer = x + 4
• Sixth Integer = x + 5
• Seventh Integer = x + 6
• Eighth Integer = x + 7
• Ninth Integer = x + 8
• Tenth integer = x + 9
• Eleventh Integer = x + 10

ATQ,

☞ x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 + x + 6 + x + 7 + x + 8 + x + 9 + x + 10 = 2013

☞ 11x + 55 = 2013

☞ 11x = 2013 - 55

☞ 11x = 1958

☞ x = 1958/11

= 178

Hence, the smallest integer is 178.