Question

9 formula sheet matching: drag and drop the correct formulas as it is on the formula sheet. arithmetic sequence formulas recursive: $\square = \square \square$ explicit: $\square = \square \square \square$ drag & drop the answer $a_{n - 1}$ $(n + 1)$ $a_1$ $+d$ $a_{n + 1}$ $(n - 1)$ $a_n$ $-d$ note: use ctrl+d to drag the option via keyboard

Explanation:

Step1: Recursive Formula

In an arithmetic sequence, the recursive formula defines each term as the previous term plus the common difference \( d \). So the recursive formula is \( a_{n + 1}=a_{n}+d \). So we match \( a_{n + 1} \), \( a_{n} \), and \( +d \) for the recursive part.

Step2: Explicit Formula

The explicit formula for an arithmetic sequence is \( a_{n}=a_{1}+(n - 1)d \). So we match \( a_{n} \), \( a_{1} \), and \( (n - 1) \) (along with the \( +d \) conceptually, but in terms of the drag - and - drop, the components are \( a_{n} \), \( a_{1} \), and \( (n - 1) \) with the operation of multiplication by \( d \) implied in the formula structure).

Answer:

Recursive: \( a_{n + 1}=a_{n}+d \) (Drag \( a_{n + 1} \) to the first box, \( a_{n} \) to the second box, \( +d \) to the third box)
Explicit: \( a_{n}=a_{1}+(n - 1)d \) (Drag \( a_{n} \) to the first box, \( a_{1} \) to the second box, \( (n - 1) \) to the third box)