Find sum of the first eight terms of the geometric series; 3+6+12+…
To find the sum of the first eight terms of a geometric series, we can use the formula:
\[ S_n = \frac{a(1 – r^n)}{1 – r} \]
where:
– \( S_n \) is the sum of the first n terms,
– \( a \) is the first term,
– \( r \) is the common ratio,
– \( n \) is the number of terms
To find the sum of the first eight terms of a geometric series, we can use the formula:
\[ S_n = \frac{a(1 – r^n)}{1 – r} \]
where:
– \( S_n \) is the sum of the first n terms,
– \( a \) is the first term,
– \( r \) is the common ratio,
– \( n \) is the number of terms.
In this case, the first term, \( a \), is 3. The series has a common ratio of 2, as each term is double the previous term.
Let’s substitute these values into the formula:
\[ S_8 = \frac{3(1 – 2^8)}{1 – 2} \]
Now, simplify the formula:
\[ S_8 = \frac{3(1 – 256)}{-1} \]
\[ S_8 = \frac{3(-255)}{-1} \]
\[ S_8 = \frac{-765}{-1} \]
\[ S_8 = 765 \]
Therefore, the sum of the first eight terms of the geometric series is 765.
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