What is comparable pay?

30 days: on 1st day pay is .01, 2nd day pay is .02, etc (pay doubles each day) what's total pay in 30 days?

• A temporary worker is hired for 30 days. The pay on first day is 1 cent, on the second day its 2 cents, and the pay doubles each day. What's the total pay for the 30 days work?

• Answer:

  The sequence: .01, .02, .04, .08 is Geometric since each number in the sequence differs by a constant factor. The nth term of a Geometric sequence is Gn = a r^(n-1) r is then: r = An+1/ An or A2/A1 = .02 / .01 = 2 a = Gn/(r^(n-1)) = G2/r = .02/2 = 1/100 The sum of the 1st n terms of a Geometric sequence is: Sn = a(1-r^n) /( 1-r) check: G1 = 1/100 = .01 check: G2 = 1/50 = .02 check: G3 = 1/25 = .04 check: G4 = 2/25 = .08 S30 = 1/100 * (1 - 2^30) / (1-2) = 10737418.23 nice job if you can get it.