Solution - Geometric Sequences

To find the general form of the series, plug the first term: $$a=673$$ and the common ratio: $$r=0.3803863298662704$$ into the formula for geometric series:

$$a_1=673$$

$$a_2=a_1·r^{n-1}=673\cdot {0.3803863298662704}^{2-1}=673\cdot {0.3803863298662704}^1=673\cdot 0.3803863298662704=256$$

$$a_3=a_1·r^{n-1}=673\cdot {0.3803863298662704}^{3-1}=673\cdot {0.3803863298662704}^2=673\cdot 0.14469375994913108=97.37890044576523$$

$$a_4=a_1·r^{n-1}=673\cdot {0.3803863298662704}^{4-1}=673\cdot {0.3803863298662704}^3=673\cdot 0.05503952830160112=37.04160254697756$$

$$a_5=a_1·r^{n-1}=673\cdot {0.3803863298662704}^{5-1}=673\cdot {0.3803863298662704}^4=673\cdot 0.02093628416821677=14.090119245209886$$

$$a_6=a_1·r^{n-1}=673\cdot {0.3803863298662704}^{6-1}=673\cdot {0.3803863298662704}^5=673\cdot 0.00796387629578528=5.359688747063493$$

$$a_7=a_1·r^{n-1}=673\cdot {0.3803863298662704}^{7-1}=673\cdot {0.3803863298662704}^6=673\cdot 0.003029349675662751=2.0387523317210317$$

$$a_8=a_1·r^{n-1}=673\cdot {0.3803863298662704}^{8-1}=673\cdot {0.3803863298662704}^7=673\cdot 0.0011523232050069305=0.7755135169696642$$

$$a_9=a_1·r^{n-1}=673\cdot {0.3803863298662704}^{9-1}=673\cdot {0.3803863298662704}^8=673\cdot 0.0004383279947723242=0.2949947404817742$$

$$a_{10}=a_1·r^{n-1}=673\cdot {0.3803863298662704}^{10-1}=673\cdot {0.3803863298662704}^9=673\cdot 0.00016673397720908616=0.11221196666171498$$