Answer
$a_{n}= 0.10 (2)^{n-1}$
$819.20 $ Dollars
Work Step by Step
Allowance on first day
$a_{1}= 0.10 = 0.10 \times 1 = 0.10 \times 2 ^{0}$
Allowance on second day
$a_{2}= 0.20 =0.10 \times 2 = 0.10 \times 2 ^{1}$
Allowance on third day
$a_{3}= 0.40 =0.10 \times 4 = 0.10 \times 2 ^{2} $
Allowance on fourth day
$a_{4}= 0.80 =0.10 \times 8 = 0.10 \times 2 ^{3} $
Allowance on nth day
$a_{n}= 0.10 \times 2 ^{n-1} $
Allowance on 14th day
$a_{14}= 0.10 \times 2 ^{14-1} $
$a_{14}= 0.10 \times 2 ^{13} $
$a_{14}=0.10 \times 8192$
$a_{14}= 819.20$ Dollars
