Question

6.6 comparing linear and exponential functions (sequences) quiz

an explicit formula allows you to find any term directly.

true
false

Explanation:

Define explicit formulas in sequences

Using the Explicit Formula knowledge point
An explicit formula defines the \(n\)-th term of a sequence, \(a_n\), as a direct function of its position \(n\). This allows you to calculate any term in the sequence immediately without needing to know or calculate any of the preceding terms.

Compare with recursive formulas

Using the Explicit Formula knowledge point
Unlike a recursive formula, which requires calculating all previous terms (e.g., \(a_n = a_{n-1} + d\)), an explicit formula (e.g., \(a_n = a_1 + (n-1)d\)) allows direct evaluation for any term index \(n\). Therefore, the statement is true.

Answer:

• True (Correct answer)
• False