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.
A(n)=- 3+(n-1)2.5
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+2.5 ⟶- 0.5+2.5 ⟶2+2.5 ⟶4.5...
By substituting these two values into the explicit equation and simplifying, we can find the formula for this sequence.
