For what value of n are the nth terms of two A.P's 63 , 56 , 67 , ....... and 3 , 10 , 17 .......equal?===============================================The diameter of a roller 120cm long is 84cm . If it takes 500 complete revolutions to level a playground , determine the cost of levelling it at the rate of 30 paise per square metre.

For what value of n are the nth terms of two A.P's 63 , 56 , 67 , ....

1.	For what value of n are the nth terms of two A.P's 63 , 56 , 67 , ....... and 3 , 10 , 17 .......equal?===============================================The diameter of a roller 120cm long is 84cm . If it takes 500 complete revolutions to level a playground , determine the cost of levelling it at the rate of 30 paise per square metre.
Answer» I think there is a typing mistake : it is 65 INSTEAD of 56. 1st series: 63, 65, 67 ... : common diff = d = 2 a = 63 Tn = 63 + (n-1) 2 = 2 n + 61 2nd series : 3, 10 , 17,.. : d = 7 a = 3 Tn = 3 + (n-1) 7 = 7 n - 4 so 2 n + 61 = 7n - 4 5n = 65 => n = 13 ================================ S = curved surface area of the cylinder = 2 π R L radius = R = 84/2 = 42 cm L = length = 120 cm S = 2 π 0.42 m * 1.20 m = 3.166 m² 500 complete turns => area rolled = 500 * S = 1583.36 m² Cost = 1583.36 * 30/100 = RS 475