SOLVING WORD PROBLEMS USING ARITHMETIC PROGRESSION

Problem 1 :

Subba Rao started work in 1995 at an annual salary of $ 5000 and received and increment of 200 each year. In which year did his income reach $ 7000

Solution :

5000, 5200,,...........7000

a = 5000, d = 5200 - 5000  =  200, a_n = 7000 

 a_n = a + (n - 1) d

 7000  =  5000 + (n - 1) 200

 7000 - 5000  =  (n - 1) 200 

2000  =  (n - 1) 200

n - 1  =  2000/200

n - 1  =  10

n  =  10 + 1

n  =  11

So, 11^th year his salary will be 7000.

Problem 2 :

John saved $5 in the first week of a year and then increased her weekly savings by $1.75. If the n^th week, her weekly savings become $20.75, find n.

Solution :

a = 5  d = 1.75  an = 20.75

 a_n = a + (n - 1) d

 20.75 = 5 + (n - 1) 1.75

 20.75 - 5 = (n - 1) 1.75

  15.75 = ( n - 1) 1.75

  15.75/1.75 = n - 1

   9 = n - 1

   n - 1 = 9

    n = 9 + 1

    n = 10

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