Question

How many arithmetic progression can have any 3 terms as 1,3,1000.

Answer 1

There can be infinite AP which can have these three terms

for example

0,1,2,3,4,..........1000 (common difference 1)

0,0.5,1,1.5,2,2.5,3,3.5.......1000 (common difference 0.5)

$0,\frac{1}{3},\frac{2}{3},1,\frac{4}{3},\frac{5}{3},\mathrm{2...3......1000}$ (common difference \(\frac{1}{3})