Arithmetic Sequence
An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant
An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. This difference is also known as the common difference. In other words, to go from one term to the next, you always add or subtract the same value.
To understand arithmetic sequences better, let’s take an example.
Consider the sequence: 2, 5, 8, 11, 14, …
In this sequence, the common difference is 3 since you add 3 to each term to get to the next term. The first term of the sequence is 2.
One important property of arithmetic sequences is that you can find the nth term of the sequence using a formula.
The formula for the nth term of an arithmetic sequence is:
an = a1 + (n – 1)d
Where:
– an is the nth term of the sequence,
– a1 is the first term of the sequence,
– n is the position of the term you want to find,
– d is the common difference.
Let’s see how this formula can be used to find the 5th term of the sequence mentioned earlier.
a5 = a1 + (5 – 1)d
= 2 + (4)(3)
= 2 + 12
= 14
So, the 5th term of the sequence is 14.
Similarly, you can find any term in the sequence by plugging in the appropriate values for a1, n, and d into the formula.
Arithmetic sequences are widely used in mathematics and have many real-world applications, such as calculating salary increments, population growth, and financial analysis.
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