Question

For what value of n are the nth terms of two A.P's 63 , 56 , 67 , ....... and 3 , 10 , 17 .......equal?

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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 1

first ap=63,56,49...
f=63
d=-7
xn=dn+(f-d)
  = -7n+(63--7)
  = -7n+70
second a.p= 3,10,17..
f=3
d=7
xn=dn+(f-d)
  = 7n+(3-7)
  =7n-4
7n-4= -7n+70
14n-4=70
14n=74
n=74/14
n is not a natural number so there isn't common term

Answer 2

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
 
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 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