A set of objects, including numbers or letters in a certain order, is known as a sequence in mathematics. The sequence's objects are known as terms or elements. It is quite normal to see the same object in one sequence many times.
Arithmetic sequence definition can be interpreted as:
"A set of objects that comprises numbers is an arithmetic sequence. A constant number known as the common difference is applied to the previous number to create each successive number."
The common difference refers to the difference between any two consecutive terms of the sequence.
We can use the arithmetic sequence formula to find any term in the sequence. Arithmetic sequence equation can be written as:
\(a_n = a_1 + (n-1)d\)
In this equation:
\(a_n\) refers to the \(n^{th}\) term of the sequence,
\(a_1\) refers to the first term of the sequence,
\(d\) refers to the common difference and
\(n\) refers to the length of the sequence.
The above formula is an explicit formula for an arithmetic sequence. All terms are equal to each other if there is no common difference in the successive terms of a sequence. In this case, there would be no need for any calculations.
Find the 10^{th} term in the below sequence by using the arithmetic sequence formula.
\(2, 4, 6, 8, 10, 12, 14, 16, 18...\)
As we know, n refers to the length of the sequence, and we have to find the 10^{th} term in the sequence, which means the length of the sequence will be 10. Follow these steps to find a specific term in an arithmetic sequence.
Step 1: Write down the sequence.
\(2, 4, 6, 8, 10, 12, 14, 16, 18...\)
Step 2: Find the common difference d.
\(d = n_2 - n_1\)
\(d = 2\)
Step 3: Write down the formula of the arithmetic sequence.
\(a_n = a_1 + (n-1)d\)
Step 4: Substitute the values in the equation.
As we know,
\(a_1= 2, n = 10,\) and \(d = 2\)
\(a_{10} = 2 + (10 - 1) 2 = 20\)
So the 10^{th} term of this arithmetic sequence would be 20. You can also use our above arithmetic sequence formula calculator to find the required value.
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