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The expression n(n - 1) represents a quadratic sequence. To find the first four terms, we can substitute n = 1, 2, 3, and 4.

  • For n = 1: 1(1 - 1) = 0
  • For n = 2: 2(2 - 1) = 2
  • For n = 3: 3(3 - 1) = 6
  • For n = 4: 4(4 - 1) = 12

Thus, the first four terms are 0, 2, 6, and 12.

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What is the sum of the first six terms of the geometric sequence 1 4 16?

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 are the first 5 terms of n plus 3?

The expression "n plus 3" can be represented as ( n + 3 ). To find the first five terms, we can substitute the values ( n = 1, 2, 3, 4, ) and ( 5 ) into the expression. The first five terms are: ( 1 + 3 = 4 ) ( 2 + 3 = 5 ) ( 3 + 3 = 6 ) ( 4 + 3 = 7 ) ( 5 + 3 = 8 ) Thus, the first five terms are 4, 5, 6, 7, and 8.


What is the rule to this pattern 1 3 4 7 11 18?

This is a Fibonacci sequence where the first two terms are known as 'seed values' and successive terms are the sum of the two previous terms. 4 = 3 + 1 7 = 4 + 3 11 = 7 + 4 18 = 11 + 7.


What is k plus 1 plus k plus 4 simplified?

The expression ( k + 1 + k + 4 ) can be simplified by combining like terms. First, combine the ( k ) terms: ( k + k = 2k ). Then, combine the constant terms: ( 1 + 4 = 5 ). Therefore, the simplified expression is ( 2k + 5 ).

Related Questions

What is the sum of the first six terms of the geometric sequence 1 4 16?

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 ).


What are the first 3 terms for 4n plus 1?

As whole number integers? 4(1) + 1 = 5 ------ 4(2) + 1 = 9 ----- 4(3) + 1 = 13 -------


What were Louis Joliet's 4 voyages?

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Is 1 over 4 lowest terms?

Yes, 1/4 is in its lowest terms


What is 1 over 4 in lowest terms?

1/4 is already in its lowest terms


What is the formula for the geometric progression with the first 3 terms 4 2 1?

The nth term of the series is [ 4/2(n-1) ].


What is the rule to this pattern 1 3 4 7 11 18?

This is a Fibonacci sequence where the first two terms are known as 'seed values' and successive terms are the sum of the two previous terms. 4 = 3 + 1 7 = 4 + 3 11 = 7 + 4 18 = 11 + 7.


What is k plus 1 plus k plus 4 simplified?

The expression ( k + 1 + k + 4 ) can be simplified by combining like terms. First, combine the ( k ) terms: ( k + k = 2k ). Then, combine the constant terms: ( 1 + 4 = 5 ). Therefore, the simplified expression is ( 2k + 5 ).


What are the first 5 terms in the sequence 3n-3?

To find the first 5 terms, plug 1, 2, 3, 4 and 5 in for n:3*1-3 = 03*2-3 = 33*3-3 = 63*4-3 = 93*5-3 = 12The first five terms are 0, 3, 6, 9 and 12.


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