
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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April 11th, 2018, 10:36 PM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  Why we should divide with 2 in third step?
The annual income of Pradeep is the year 2001 was 240000. Starting from 2002, his annual income increased by 36000 every year over the proceeding year. What was the average annual of Pradeep for the years 2001 to 2008? Solution: The annual income of Pradeep is the year 2001 = 240000 The annual income of Pradeep in 2008 = 240000 + 7 (36000) = 492000 Total income in 8 years = $\displaystyle \frac {8}{2} [240000+492000]= 2928000$ Required average annual income is $\displaystyle \frac {2928000}{8} = 366000$ Why we should divide with 2 in third step? Last edited by Ganesh Ujwal; April 11th, 2018 at 10:41 PM. 
April 12th, 2018, 04:39 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 
Since the annual income is increasing by the same number each year, it is an "arithmetic sequence" (a, a+ b, a+ 2b, a+ 3b, ...). It is a property of an arithmetic sequence that the average of all numbers in the sequence is the same as the average of the first and last numbers in the sequence. That is what they are doing here. The first number in the sequence is the first annual income, 240000. The last number is the annual income 7 years later, 240000 + 7 (36000) = 492000. The average annual income is (240000+ 492000)/2= 732000/2= 366000. The total income over those eight years is that average multiplied by 8: 8(366000)= 2928000. We divide by 2 in the third step because we are really taking the average of two numbers. 
April 12th, 2018, 08:28 AM  #3 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  

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