Explicit equations for arithmetic sequences follow a specific format.
a_n= a_1+( n-1) d
In this form, a_1 is the first term in a given sequence, d is the common difference from one term to the next, and a_n is the {\color{#FF0000}{n}}^\text{th} term in the sequence. For this exercise, the first term is a_1= 4. Let's observe the other terms to determine the common difference d.
4+1 →5+1 →6+1 →7...
By substituting these two values into the explicit equation and simplifying, we can find the formula for this sequence.
This equation can be used to find any term in the given sequence. To find a_(25), the {\color{#FF0000}{25}}^\text{th} term in the sequence, we substitute 25 for n.
Another common type of sequence is a geometric sequence, which has a common ratio instead of a common difference — the consecutive numbers are multiplied by the same number each time instead of having the same number added to them.
