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April 11th, 2018, 09:36 PM   #1
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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 09:41 PM.
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April 12th, 2018, 03:39 AM   #2
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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.
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April 12th, 2018, 07:28 AM   #3
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Quote:
Originally Posted by Country Boy View Post
S 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.
Why did you calculate average two times? Why not calculate eight years average directly?
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