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The sequence is a collection of objects in which repetitions are allowed and order is important.
What are the Different Types of Sequences?
Arithmetic sequence: A sequence in which every successive term differs from the previous one is constant, is called Arithmetic Sequence.
E.g. Suppose in a sequence a1, a2, a3, …., an are the terms & difference between each term is ‘d’, then the formula is given by an = a1 + (n−1)d
Geometric Sequence: A sequence in which every successive term has a constant ratio is called Geometric Sequence.
E.g. Suppose in a sequencea1, a2, a3, …., anare the terms & ratio between each term is ‘r’, then the formula is given byan=(an – 1) × r
Harmonic Sequence: It is a series formed by taking the inverse of arithmetic series.
E.g. Harmonic series looks like this 1/a1, 1/a2, 1/a3, ……. Where a2 = a1 + d ; a3 = a2 + d & so on…
Fibonacci Sequence: A sequence in which two consecutive terms are added to get the next consecutive 3rd term is called Fibonacci Sequence.
E.g. Suppose in a sequence a1, a2, a3, …., anare the terms & a3 = a2 + a1 & so on…. Formula is given by an = an-2 + an-1, n > 2
Sequence of Prime Numbers: A prime number is a number that is not divisible by any other number except one & that number, this sequence is infinite, never-ending.
E.g. This is a sequence of prime numbers – 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, ….. & so on
Second Degree Polynomial: It is a polynomial where the highest degree of a polynomial is 2. It is also called a quadratic polynomial.
E.g. It is represented in the form as f(x)=Ax^2+Bx+C, where A, B, C are constants. Understand the concept in more detail with the explanations and procedure listed for Sequences. Visit sequencecalculators.com, the best place for learning, and get various calculators for making your job easier.
The steps for finding the formula of a given arithmetic sequences are given below:
Step 1: Find the difference consecutive terms in the sequence & check whether the difference is the same for each pair of terms. For example, consider a sequence 3,17,? ,45....
Step 2: Heck for missing numbers by checking the difference. It should be the same in every case. Wherever it is not, we can add the common difference to the number before the space of the missing number in the sequence.
In the above example taking A1=3 and An=45. Assuming the sequence as Arithmetic Sequence and solving for d, the common difference, we get,
45 = 3 + (4-1)d
14 = d
Hence, by adding 14 to the successive term, we can find the missing term.
Step 3: Repeat the above step to find more missing numbers in the sequence if there.
Step 4: We can check our answer by adding the difference, “d” to each term in the sequence to check whether the next term in the sequence is correct or not.
Step 5: After finding the common difference for the above-taken example, the sequence becomes 3, 17, 31, 45..... and the missing term is 31. Hence, we can state that the given sequence is Arithmetic Sequence.
Step 6: After finding the type of Sequence. We can easily determine the formula