In an A.P. 19th term is 52 and 38th term is 128, find first terms and common difference​

2 thoughts on “In an A.P. 19th term is 52 and 38th term is 128, find first terms and common difference​”

1. Term difference = (position difference) × common difference.

   128 – 52 = (38 – 19)×c.d

   76 = 19×c.d

   Common difference = 76/19 = 4

   So, first term = 19th term – 18×c.d = 52-72

   = -20

   Hope it helps. Thank you.

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2. Answer:

   let the 1st term is a

   common difference is d

   then 19th term=a+(19-1).d=52

   => a+18d=52

   again ,

   38th term=a+(38-1)d=128

   => a+37d=128

   subtracting,

   18d-37d=52-128

   => -19d= -76

   => d= -76/-19

   => d=4

   a+18d=52

   => a+18.4=52

   => a+72=52

   => a= 52-72

   => a = -20

   so 1st term is -20 and common difference is 4

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