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It is the start of an arithmetic sequence.
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What is the 33rd term of this arithmetic sequence 12 7 2 -3 -8 and?
It is -148.
Descending arithmetic sequence?
An arithmetic sequence is where a constant is added to the base case, and then added again until the proscribed limit is reached. An example is 1, 3, 5, 7, where the constant is 2 and the base case is 1. The constant can be negative, such as -4, base case 16, which leads to a descending sequence of 16 12 8 4 0 -4 -8...
What is the sequence of 10 8 6 4?
10-2x for x = 0, 1, 2, 3, ... Since the domain of an arithmetic sequence is the set of natural numbers, then the formula for the nth term of the given sequence with the first term 10 and the common difference -2 is an = a1 + (n -1)(-2) = 10 - 2n + 2 = 12 - 2n.
What is the answer for finding the sum of the arithmetic sequence with a sigma notation with a 25 on top and t1 on the bottom then 5t-3 on the rightside?
To find the sum of 25 terms of these arithmetic sequence you can use the formula:Sn = (n/2)(a1 + an), where n is the number of terms in the sequence, a1 is the first term, and an is the last term of the sequence. In our case n = 25, so we need to compute a1 and a25.Since an = 5t - 3, thena1 = 5(1) - 3 = 5 - 3 = 2a25 = 5(25) - 3 = 125 - 3 = 122By substituting the values we know into the formula we have:S25 = (25/2)(2 + 122) = (25/2)(124) = 25 x 62 = 1,550Or you can use the formula:Sn = (n/2)[2a1 + (n - 1)d] where d is the common difference.In order to find d, we need to find at least the value of 2 terms and subtract them.a1 = 2a2 = 5(2) - 3 = 10 - 3 = 7So d = 7 - 2 = 5By substituting the values we know into the formula we have:S25 = (25/2)[2(2) + (25 - 1)5]S25 = (25/2)(4+ 120) = (25/2)(124 = 25 x 62 = 1,550Thus, the sum of 25 terms of the given arithmetic sequence is 1,550.
What is a sum of a sequence?
If 1,2,3,4,5, is a sequence, then the sum is 1+2+3+4+5 = 15
Who was the founder of arithmetic sequence?
One of the simplest arithmetic arithmetic sequence is the counting numbers: 1, 2, 3, ... . The person who discovered that is prehistoric and, therefore, unknown.
What describes the sequence 1 1 2 3 5 is it arithmetic or geometric?
It is an arithmetic sequence. To differentiate arithmetic from geometric sequences, take any three numbers within the sequence. If the middle number is the average of the two on either side then it is an arithmetic sequence. If the middle number squared is the product of the two on either side then it is a geometric sequence. The sequence 0, 1, 1, 2, 3, 5, 8 and so on is the Fibonacci series, which is an arithmetic sequence, where the next number in the series is the sum of the previous two numbers. Thus F(n) = F(n-1) + F(n-2). Note that the Fibonacci sequence always begins with the two numbers 0 and 1, never 1 and 1.
Is 2 6 18 54 an arithmetic sequence?
No it is not.U(2) - U(1) = 6 - 2 = 4U(3) - U(2) = 18 - 6 = 12Since 4 is different from 12, it is not an arithmetic sequence.
Can a recursive formula produce an arithmetic or geometric sequence?
arithmetic sequence * * * * * A recursive formula can produce arithmetic, geometric or other sequences. For example, for n = 1, 2, 3, ...: u0 = 2, un = un-1 + 5 is an arithmetic sequence. u0 = 2, un = un-1 * 5 is a geometric sequence. u0 = 0, un = un-1 + n is the sequence of triangular numbers. u0 = 0, un = un-1 + n(n+1)/2 is the sequence of perfect squares. u0 = 1, u1 = 1, un+1 = un-1 + un is the Fibonacci sequence.
Is the sequence 2 3 5 8 12 arithmetic or geometric?
It is neither. It is a quadratic sequence. Un = (x2 - x + 4)/2 for n = 1, 2, 3, ...
What sequence does the arithmetic variable 5n plus 2 represent?
Put n = 1, 2, 3, 4 etc in the expression 5n + 2 and evaluate to get the sequence.
What is the next term in this arithmetic sequence 11 8 5 2 ...?
-1 deduct 3 each time
What are the numbers whose sum is 3 form an arithmetic sequence and their squares form geometric sequence?
The numbers are: 1-sqrt(2), 1 and 1+sqrt(2) or approximately -0.414214, 1 and 2.414214
What is the nth term for 3 5 7 9?
This is an arithmetic sequence with initial term a = 3 and common difference d = 2. Using the nth term formula for arithmetic sequences an = a + (n - 1)d we get an = 3 + (n - 1)(2) = 2n - 2 + 3 = 2n + 1.
The sum of the first 5 terms of an arithmetic sequence is 40 and the sum of its first ten terms is 155what is this arithmetic sequence?
a1=2 d=3 an=a1+(n-1)d i.e. 2,5,8,11,14,17....
Find the 19th term of the arithmetic sequence -4, -1 1/3, 1 1/3, 4?
The 19th term of the sequence is 16.
Can a sequence of numbers be both geometric and arithmetic?
Yes, it can both arithmetic and geometric.The formula for an arithmetic sequence is: a(n)=a(1)+d(n-1)The formula for a geometric sequence is: a(n)=a(1)*r^(n-1)Now, when d is zero and r is one, a sequence is both geometric and arithmetic. This is because it becomes a(n)=a(1)1 =a(1). Note that a(n) is often written anIt can easily observed that this makes the sequence a constant.Example:a(1)=a(2)=(i) for i= 3,4,5...if a(1)=3 then for a geometric sequence a(n)=3+0(n-1)=3,3,3,3,3,3,3and the geometric sequence a(n)=3r0 =3 also so the sequence is 3,3,3,3...In fact, we could do this for any constant sequence such as 1,1,1,1,1,1,1...or e,e,e,e,e,e,e,e...In general, let k be a constant, the sequence an =a1 (r)1 (n-1)(0) with a1 =kis the constant sequence k, k, k,... and is both geometric and arithmetic.
