What is the first term of the sequence? What is the common difference between terms? Use these values in the explicit equation for arithmetic sequences.
B
Practice makes perfect
Explicit equations for arithmetic sequences follow a specific format.
a_n= a_1+( n-1) dIn 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= 3. Let's observe the other terms to determine the common difference d.
3+5 →8+5 →13+5 →18+5 →23...
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. We can write it also as a function of n. Then the function is expressed as A(n)=3+(n-1)(5), which corresponds to the answer B.
