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Reika [66]
4 years ago
10

Find the sum of the first 8 terms of the series. 1/2 + 1 + 2 + 4

Mathematics
2 answers:
Fynjy0 [20]4 years ago
5 0

Answer:

The sum of 8 term of the series is \dfrac{255}{2} or 127.5

Step-by-step explanation:

Given: The series \frac{1}{2} + 1 +2 +4 + ...

We need to find the sum of 8 term

Common ratio, r =\dfrac{2}{1}= 2

First term, a=\dfrac{1}{2}

n=8

Formula:

S_n=\dfrac{a(r^n-1)}{(r-1)}

Substitute the value of a, r and n into formula

Sum of 8th term of the sequence

S_8=\dfrac{1/2(2^8-1)}{2-1}

S_8=\dfrac{255}{2}

Hence, The sum of 8 term of the series is \dfrac{255}{2} or 127.5

Roman55 [17]4 years ago
4 0

\bf \cfrac{1}{2}~~,~~\stackrel{2\cdot \frac{1}{2}}{1}~~,~~\stackrel{2\cdot 1}{2}~~,~~\stackrel{2\cdot 2}{4}~~,...

so as you can see the common ratio is 2, and the first term is 1/2,

\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad  \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ r=2\\ a_1=\frac{1}{2}\\ n=8 \end{cases} \\\\\\ S_8=\cfrac{1}{2}\left( \cfrac{1-2^8}{1-2} \right)\implies S_8=\cfrac{1}{2}\left( \cfrac{-255}{-1} \right)\implies S_8=\cfrac{255}{2}

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