Question

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

Answer 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.

Answer 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