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The given series appears to follow a pattern where each term can be expressed in the form of a quadratic sequence. The nth term can be represented as ( a_n = n(3n - 2) ). To find the sum of the first n terms, ( S_n ), we can derive it from the formula for the sum of a quadratic sequence, leading to ( S_n = \frac{n}{6}(n + 1)(n + 2) ). Thus, the sum to n terms of the series is given by this formula.
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What is the sum of the first five terms of a geometric series with a1 20 and r 14?
To find the sum of the first five terms of a geometric series, we use the formula ( S_n = a_1 \frac{1 - r^n}{1 - r} ), where ( a_1 ) is the first term, ( r ) is the common ratio, and ( n ) is the number of terms. Here, ( a_1 = 20 ), ( r = 14 ), and ( n = 5 ). Plugging in the values, we get: [ S_5 = 20 \frac{1 - 14^5}{1 - 14} = 20 \frac{1 - 537824}{-13} = 20 \cdot \frac{-537823}{-13} = 20 \cdot 41401 = 828020. ] Thus, the sum of the first five terms is 828020.
What expression defines the given series for seven terms of this sequence -4 (-5) (-6) ...?
The given series is an arithmetic sequence where the first term is -4 and the common difference is -1. The seven terms can be expressed as -4, -5, -6, -7, -8, -9, -10. The expression for the sum of these seven terms can be calculated using the formula for the sum of an arithmetic series: ( S_n = \frac{n}{2} (a + l) ), where ( n ) is the number of terms, ( a ) is the first term, and ( l ) is the last term. Here, ( S_7 = \frac{7}{2} (-4 + (-10)) = \frac{7}{2} (-14) = -49 ).
What comes next and why 3 1 4 5 9 14 23 37?
These are numbers where after the second number each one is the sum of the previous two. So then you have 23+37 = 60, then 37+60 etc. Eventually you get a series where successive terms are in the same ratio as for the Fibonacci series.
What is the sum of 14 and 9?
The sum of 14 and 9 is 23.
What does the word sum mean in maths?
The term "sum" implies the answer to addition.Example: What is the sum of 10 and 14? The sum is 24.10 + 14 = 24
What is 510 -14?
510 -14 = 496
What is the sum of the first five terms of a geometric series with a1 20 and r 14?
To find the sum of the first five terms of a geometric series, we use the formula ( S_n = a_1 \frac{1 - r^n}{1 - r} ), where ( a_1 ) is the first term, ( r ) is the common ratio, and ( n ) is the number of terms. Here, ( a_1 = 20 ), ( r = 14 ), and ( n = 5 ). Plugging in the values, we get: [ S_5 = 20 \frac{1 - 14^5}{1 - 14} = 20 \frac{1 - 537824}{-13} = 20 \cdot \frac{-537823}{-13} = 20 \cdot 41401 = 828020. ] Thus, the sum of the first five terms is 828020.
What expression defines the given series for seven terms of this sequence -4 (-5) (-6) ...?
The given series is an arithmetic sequence where the first term is -4 and the common difference is -1. The seven terms can be expressed as -4, -5, -6, -7, -8, -9, -10. The expression for the sum of these seven terms can be calculated using the formula for the sum of an arithmetic series: ( S_n = \frac{n}{2} (a + l) ), where ( n ) is the number of terms, ( a ) is the first term, and ( l ) is the last term. Here, ( S_7 = \frac{7}{2} (-4 + (-10)) = \frac{7}{2} (-14) = -49 ).
What comes next and why 3 1 4 5 9 14 23 37?
These are numbers where after the second number each one is the sum of the previous two. So then you have 23+37 = 60, then 37+60 etc. Eventually you get a series where successive terms are in the same ratio as for the Fibonacci series.
How old is a CTK 510 casio piano?
14 years
How old is a CTK-510 casio piano?
14 years
What is the sum for tetrakaidecagon interior angle?
On the basis that you are familiar with terms such as "tetrakaidecagon" I assume you are mathematically at a stage where angles are measured in radians and not degrees. Then the interior angles of a 14 sided polygon sum to (14-2)*pi radians or 12*pi radians.
What is the sum of 14 and 9?
The sum of 14 and 9 is 23.
What is the sum of -14 plus 29?
the sum of -14 + 29 is 15
What does the word sum mean in maths?
The term "sum" implies the answer to addition.Example: What is the sum of 10 and 14? The sum is 24.10 + 14 = 24
The sum of 14 and the sum of 8?
You can't take a sum if you only have one number. If you mean the sum of 14 and 8, well, just add them... 14 + 8 = 22... XD
What is the sum of the pH and pOH in a substance.?
The sum is 14 at room temperature.
