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# aritmetic progression

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473
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find the 20th term from the last term of the A.P: 3,8,13,,,,,253

SARAHann  Mar 22, 2017
#1
+12735
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Common difference between terms is  5       (8-3 = 5      13-8 = 5 etc)

this is of the form    3 + 5 (n-1)

3 + 5n -5 = 5n-2         where n= number of the term

20th term       5(20)-2 = 98

ElectricPavlov  Mar 22, 2017
#2
+302
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can we find the answer by reversing the A.P?

SARAHann  Mar 22, 2017
#3
+88899
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Good idea.....!!!

The last term  is   253

And the common difference in terms is 5

So......the 20th term from the last  =

253 - 5(n - 1) =

253 - 5(20 - 1)  =

253 - 5(19)  =

158

CPhill  Mar 22, 2017
#4
+302
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Is d= -5 or 5?

then if it's 5 shouldn't it  be 253+(n-1)*5?

SARAHann  Mar 22, 2017
#5
+88899
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I suppose that you're technically correct......the common difference is -5 [ we are subtracting 5 each time ]

CPhill  Mar 22, 2017
#8
+302
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OK I get it! thx!

SARAHann  Mar 25, 2017
#6
+12735
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I will continue the way I started

we have 5n-2  gives the nth term

253 = 5n-2

255 = 5n

yields n = 51st term for 253      20 terms before this would be 31st term

5(31)-2 = 153   = 20 terms before 253

I think Chris answer may be the 19th before 253

if you use his equation    the tem that is ONE before would be 253 - 5(1-1) = 253    which would be incorrect.

ElectricPavlov  Mar 22, 2017
#7
+88899
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OK.....thanks, EP....

CPhill  Mar 22, 2017