You start with the number 4, then multiply with the "common ratio" to get the next term. That, in turn, is multiplied by the common ratio to get the next term, etc.
A geometric sequence with 5 terms can alternate by having positive and negative terms. For example, one such sequence could be (2, -6, 18, -54, 162). Here, the first term is (2) and the common ratio is (-3), leading to alternating signs while maintaining the geometric property.
A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. For example, in the sequence 2, 6, 18, 54, the common ratio is 3. The general form of a geometric sequence can be expressed as ( a_n = a_1 \cdot r^{(n-1)} ), where ( a_1 ) is the first term, ( r ) is the common ratio, and ( n ) is the term number.
36
-1,024
The given sequence is a geometric sequence where each term is multiplied by 2 to get the next term. The first term (a) is 4, and the common ratio (r) is 2. The nth term of a geometric sequence can be found using the formula ( a_n = a \cdot r^{(n-1)} ). Therefore, the nth term of this sequence is ( 4 \cdot 2^{(n-1)} ).
Find the 7th term of the geometric sequence whose common ratio is 1/2 and whose first turn is 5
36
-1,024
11.27357
It is 1062882.
A geometric series represents the partial sums of a geometric sequence. The nth term in a geometric series with first term a and common ratio r is:T(n) = a(1 - r^n)/(1 - r)
This is a geometric sequence of the form a, ar, ar^2, ar^3, ... where a is the first term and r is the common ratio.In our case, the first term a = 2, and the common ratio r = 5.The nth term of such a sequence isan = a r^(n -1).
nth term Tn = arn-1 a = first term r = common factor
4096-20481024-512256-12864
It is a*r^4 where a is the first term and r is the common ratio (the ratio between a term and the one before it).
The geometric sequence with three terms with a sum of nine and the sum to infinity of 8 is -9,-18, and 36. The first term is -9 and the common ratio is -2.
The ball does not return to its initial height after bouncing. So the height it reaches after the first bounce will be a fraction of the initial height, etc. This is a geometric sequence with common ratio 5/8.