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The given geometric sequence is 1, 4, 16, where the first term ( a = 1 ) and the common ratio ( r = 4 ). To find the sum of the first six terms, we calculate the sixth term: ( a_6 = a \cdot r^{5} = 1 \cdot 4^5 = 1024 ). The sum of the first ( n ) terms of a geometric sequence is given by the formula ( S_n = a \frac{r^n - 1}{r - 1} ). Thus, the sum of the first six terms is ( S_6 = 1 \cdot \frac{4^6 - 1}{4 - 1} = \frac{4096 - 1}{3} = \frac{4095}{3} = 1365 ).
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What is first term of a geometric series is 3 and the sum of the first term and the second term is 15 What is the sum of the first six terms?
In a geometric series, if the first term ( a ) is 3 and the sum of the first and second terms is 15, we can denote the common ratio as ( r ). Therefore, we have ( 3 + 3r = 15 ), which simplifies to ( 3r = 12 ) or ( r = 4 ). The sum of the first six terms can be calculated using the formula ( S_n = a \frac{1 - r^n}{1 - r} ). Substituting ( a = 3 ), ( r = 4 ), and ( n = 6 ), we get ( S_6 = 3 \frac{1 - 4^6}{1 - 4} = 3 \frac{1 - 4096}{-3} = 4095 ).
What is next in the sequence OTTFFSS and why?
E its the first letter of the number sequence one, two three four five six seven Eight
What are the first six numbers in the Fibonacci sequence?
1, 1, 2, 3, 5, 8
How many shapes does a cube have?
A cube has one distinct shape, which is characterized by its six equal square faces, twelve edges, and eight vertices. While it can be oriented in various ways, maintaining its geometric properties, its fundamental shape remains unchanged. Thus, in terms of geometric classification, a cube is a single shape.
Can you draw a hexagon?
A hexagon is a geometric shape with six sides. To draw one, draw a polygon with six sides.
What are the first six terms of the sequence that starts with 1 and for which the consecutive terms are 2 and then 345 and 6?
123456
What is the sum of first six terms of a sequence whose nth term is 8 - n?
nth term is 8 - n. an = 8 - n, so the sequence is {7, 6, 5, 4, 3, 2,...} (this is a decreasing sequence since the successor term is smaller than the nth term). So, the sum of first six terms of the sequence is 27.
What is the next in this sequence 112358?
There are many possible answers. One obvious one is 13, the next number in the Fibonacci Sequence that yields the golden mean.
What is first term of a geometric series is 3 and the sum of the first term and the second term is 15 What is the sum of the first six terms?
In a geometric series, if the first term ( a ) is 3 and the sum of the first and second terms is 15, we can denote the common ratio as ( r ). Therefore, we have ( 3 + 3r = 15 ), which simplifies to ( 3r = 12 ) or ( r = 4 ). The sum of the first six terms can be calculated using the formula ( S_n = a \frac{1 - r^n}{1 - r} ). Substituting ( a = 3 ), ( r = 4 ), and ( n = 6 ), we get ( S_6 = 3 \frac{1 - 4^6}{1 - 4} = 3 \frac{1 - 4096}{-3} = 4095 ).
What is the first six numbers of two?
2 and then, after the decimal point, a sequence of 0s.
What is a six-sided geometric shape called?
A hexahedron is a three-dimensional geometric shape having six sides; a hexagon is a two-dimensional six-sided shape.
What is next in the sequence OTTFFSS and why?
E its the first letter of the number sequence one, two three four five six seven Eight
What are the first six numbers in the Fibonacci sequence?
1, 1, 2, 3, 5, 8
What is the Geometric mean of the pair of numbers 2 and 18?
6 (six)
How many shapes does a cube have?
A cube has one distinct shape, which is characterized by its six equal square faces, twelve edges, and eight vertices. While it can be oriented in various ways, maintaining its geometric properties, its fundamental shape remains unchanged. Thus, in terms of geometric classification, a cube is a single shape.
Can you draw a hexagon?
A hexagon is a geometric shape with six sides. To draw one, draw a polygon with six sides.
What is the next letter in the sequence tttffss?
The sequence "tttffss" represents the first letters of the numbers one through eight: one, two, three, four, five, six, seven. The next number in the sequence is eight, which starts with the letter "e." Therefore, the next letter in the sequence is "e."
