Question

Find the sum of the finite geometric sequence whose first term is 1.2, whose ratio is 0.5, and which has five terms.

Answer 1

Answer:

Step-by-step explanation:

a = 1.2;  r = 0.5

first term = 1.2

second term= 1.2*0.5 = 0.6

Third term = 0.6*0.5=0.3

Fourth term = 0.3*0.5=0.15

Fifth term=0.15*0.5=0.075

Sum of five terms = 1.2 + 0.6 +0.3 + 0.15 + 0.075 = 2.325

Answer 2

Answer: 2.325

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Work Shown:

The shortcut way to do this is to plug a = 1.2, r = 0.5 and n = 5 into the formula below.

$S_n = \frac{a*(1-r^{n})}{1-r}\\\\S_{5} = \frac{1.2*(1-0.5^{5})}{1-0.5}\\\\S_{5} = \frac{1.2*(1-0.03125)}{1-0.5}\\\\S_{5} = \frac{1.2*(0.96875)}{0.5}\\\\S_{5} = \frac{1.1625}{0.5}\\\\S_{5} = 2.325$

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The longer way is to generate the first five terms, then add them up. To generate the terms, we multiply each term by 0.5 to get the next one.

a1 = first term = 1.2

a2 = second term = 0.6, result of multiplying 0.5 and 1.2

a3 = third term = 0.3

a4 = fourth term = 0.15

a5 = fifth term = 0.075

Now add up the five terms

a1+a2+a3+a4+a5 = 1.2+0.6+0.3+0.15+0.075 = 2.325

This method isn't too tedious since n = 5 isn't too large. For large values of n, it is better to use the formula shown in the previous section.