The sum of first ten terms of an A.P. is 155 and the sum of first two terms of a G.P. is 9. The first term of the A.P. is equal to the common ratio of the G.P. and the first term of the G.P. is equal to the common difference of the A.P. Find the two progressions.

Answer

A.P. = 2, 5, 8,… and G.P. = 3, 6, 12,…
or, `A.P. = (25)/(2), (25)/(2) + (2)/(3), (25)/(2) + 2.(2)/(3),…`
and `G.P. = (2)/(3), (2)/(3).(25)/(2), (2)/(3).((25)/(2))^(2),…, 0`