What is the sum of the geometric sequence 3/12 if there are 8 terms?

65536
Answer: The sum of the geometric progression 3, 12, 48, … if there are 8 terms is 65536.

What is the geometric sequence of 3 12?

Geometric Sequence:	Common Ratio, r:
3, 12, 48, 192, 768, 3072.	r = 4. A 4 is multiplied times each term to arrive at the next term. OR divide a2 by a1 to find the common ratio of 4.

What is the 8th term of a geometric sequence?

Since the geometric sequence is not given, let us assume the first term as a and the common ratio as r. The n th term of the geometric sequence. =a*r^(n-1) When n=8,the 8th term of the geometric sequence. =a*r^(8–1)

How do you find the next three terms in a geometric sequence?

Step 1 Find the value of r by dividing each term by the one before it. The value of r is –2. Step 2 Multiply each term by –2 to find the next three terms. ×(–2) ×(–2) ×(–2) The next three terms are 80, –160, and 320.

What is the missing term in this geometric sequence 32 ____ 128?

_,32, 64, 128 The missing term is a preceding term and comes before 32. The common ratio is 2. To obtain the missing term, divide 32 by 2. Therefore, the missing term in the geometric sequence is 16.

How do you find the geometric term?

The terms of a geometric sequence can be found by beginning with the first term and multiplying by the common ratio repeatedly.

What is the next term of the geometric sequence 3 6 12 24 blank?

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by 2 gives the next term. In other words, an=a1⋅rn−1 a n = a 1 ⋅ r n – 1 . This is the form of a geometric sequence.

How do you find the nth term of a geometric sequence?

To find the nth term of a geometric sequence: 1 Calculate the common ratio raised to the power (n-1). 2 Multiply the resultant by the first term, a. More

What are the properties of geometric sequence?

Geometric sequence properties. A geometric sequence is an ordered set of numbers, in which each consecutive number is found by multiplying the previous term by a factor called the common ratio. Just as in case of any other sequence, it can have a finite (for example 30) or an infinite number of terms.

What is a geometric sequence in layperson terms?

Now let’s see what is a geometric sequence in layperson terms. A geometric sequence is a collection of specific numbers that are related by the common ratio we have mentioned before. The ratio is one of the defining features of a given sequence, together with the initial term of a sequence.

Is there a formula for the n-th term of a geometric progression?

What we saw was the specific explicit formula for that example, but you can write a formula that is valid for any geometric progression – you can substitute the values of a₁ for the corresponding initial term and r for the ratio. The general formula for the n-th term is: where n ∈ 𝗡 means that n =1, 2, 3..