What is the first term of the sequence? What is the common difference between terms? Substitute these values into the explicit formula for arithmetic sequences.
t( n)=t( 1)+( n-1) dIn this form, t( 1) is the first term in a given arithmetic sequence, d is the common difference from one term to the next, and t( n) is the {\color{#FF0000}{n}}^\text{th} term in the sequence. For this exercise, the first term is t( 1)= 3. Let's consider the other terms to determine the common difference d.
3+7 →10+7 →17...
The common difference is d = 7. By substituting these two values into the explicit equation and simplifying, we can find the formula for this sequence.
We will solve this part the same way we solved Part A. For this part, the first term is t( 1) = 20. Let's continue by finding the common difference.
10-9 →11-9 →2...
The common difference is d = -9. By substituting these two values into the explicit equation and simplifying, we can find the formula for this sequence.
