Answered

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Find the sum of the finite geometric sequence whose first term is 0.4, whose ratio is 0.5 and which has five terms.

Sagot :

The formula for the sum of the first n-th term is

[tex]S_n=\frac{a_1(1-r^n)_{}}{1-r}[/tex]

where a_1 is the first term, r is the common ratio and n is the nth term. In our case, we have

[tex]\begin{gathered} a_1=0.4 \\ r=0.5 \\ n=5 \end{gathered}[/tex]

By substiting these values into the sum formula, we have

[tex]S_5=\frac{0.4(1-0.5^5)=}{1-0.5}[/tex]

which gives

[tex]S_5=\frac{0.4(1-0.03125)}{0.5}[/tex]

then, the answer is

[tex]S_5=0.775[/tex]

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