find the sum of the first 8th term of the Geometric progression, 1,3,9,27

Sure! Let's find the sum of the first 8 terms of the given geometric progression.

To find the sum of a geometric progression, we can use the formula:

Sum = a(1 - r^n) / (1 - r)

where:
a = first term of the geometric progression (1 in this case)
r = common ratio of the geometric progression (3 in this case)
n = number of terms in the geometric progression (8 in this case)

Plugging in the values into the formula, we have:

Sum = 1(1 - 3^8) / (1 - 3)
= 1(1 - 6561) / (1 - 3)
= 1(-6560) / (-2)
= 3280

So, the sum of the first 8 terms of the geometric progression is 3280.

But hey, you know what's funny? This geometric progression is like a roller coaster ride, going up and up! It's like riding a roller coaster after eating a jumbo-sized bag of popcorn. You start off with 1, then it's 3, then it's 9, and before you know it, BAM! It's 27! Who needs a roller coaster when you have a geometric progression to give you that adrenaline rush?

To find the sum of the first 8 terms of a geometric progression, you 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 of the geometric progression, and
- \(r\) is the common ratio.

In this case, we have the geometric progression: 1, 3, 9, 27.

The first term, \(a\), is 1, and the common ratio, \(r\), can be found by dividing any term in the sequence by its preceding term. For example:

\(r = \frac{3}{1} = 3\)
or
\(r = \frac{9}{3} = 3\)
or
\(r = \frac{27}{9} = 3\)

Since the common ratio is the same for all terms, we can use any of these values.

Now, we can substitute these values into the formula to find the sum of the first 8 terms of the progression:

\[ S_8 = \frac{1(1 - 3^8)}{1 - 3} \]

Simplifying the equation further:

\[ S_8 = \frac{1(1 - 6561)}{-2} \]

\[ S_8 = \frac{-6560}{-2} \]

\[ S_8 = 3280 \]

Therefore, the sum of the first 8 terms of the geometric progression 1, 3, 9, 27 is 3280.

To find the sum of the first n terms of a geometric progression, you can use the formula:

Sn = a * (1 - r^n) / (1 - r)

Where:
Sn is the sum of the first n terms
a is the first term of the progression
r is the common ratio between terms
n is the number of terms to be summed

In this case, the first term (a) is 1, and the common ratio (r) is 3. We want to find the sum of the first 8 terms (n = 8).

Substituting these values into the formula:

Sn = 1 * (1 - 3^8) / (1 - 3)

Simplifying the expression:

Sn = 1 * (1 - 6561) / (-2)

Sn = (1 - 6561) / -2

Sn = -6560 / -2

Sn = 3280

Therefore, the sum of the first 8 terms of the given geometric progression is 3280.

1, 3, 9, 27, 81, 243, 729, 2187 (you just had to multiply each number by 3 to get the next)..now add all of these numbers together