Question

If x=9ab where a is an integer consists of a sequence of 2014 eights and the integer b consists of a sequence of 2014 fives. What is the sum of the digits of x ?

Answer 1

Step-by-step explanation:

Given If x = 9ab where a is an integer consists of a sequence of 2014 eights and the integer b consists of a sequence of 2014 fives. What is the sum of the digits of x ?

• Let the number be x = 9ab
• So a sequence consists of 2014 eights and 2014 fives  
• Now consider a = 3 eights and b = 3 fives.
•    x = 9ab
•      = 9 x 8 x 8 x 8 x 5 x 5 x 5
•       = 4435560
• Sum will be 4 + 4 + + 5 + 5 + 6 + 0
• Consider a = 5 eights and b = 5 fives.
•      x = 9ab
•         = 9 x 8 x 8 x 8 x 8 x 8 x 5 x 5 x 5 x 5 x 5
•         = 44443555560
• Sum of digits will be 4 + 4 + 4 + 4 + 3 + 5 + 5 + 5 + 5 + 6 + 0
• Consider a = 7 eights and b = 7 fives.
• x = 9ab
•   = 9 x 8 x 8 x 8 x 8 x 8 x 8 x 8 x 5 x 5 x5 x 5 x 5 x 5 x 5
•  = 444444355555560
• = 4 + 4 + 4 + 4 + 4 + 4 + 3 + 5 + 5 + 5 + 5 + 5 + 5 + 6 + 0
• So the pattern goes on and this will be in the form of
•      4 (n – 1) + 3 + 5 (n – 1) + 6 + 0
• Where n is the number of times of 8 and 5.
• So given 2014 eights and fives, substituting this we get
•      4 (2014 – 1) + 3 + 5(2014 – 1) + 6 + 0
•      4 x 2013 + 3 + 5 x 2013 + 6 + 0
•       8052 + 3 + 10065 + 6
•            = 18126
• Therefore sum of the digits will be 18126

Reference link will be

https://brainly.in/question/23251437