Tabulate a sequence and graph its terms

If t₀ = −3, which ordered pair represents the starting term?

Move the index from 0 to 5. Match the highlighted point with the horizontal index and vertical value. Each integer setting selects one term

At index 2, which point is selected?

From recurrence to plotted terms

Begin with the given initial value. Calculate each later term from the preceding value, then pair each index with its value

1. 1Coordinates The point for tₙ is (n, tₙ). Do not swap them
2. 2Discrete domain Here n is a non-negative integer. Do not join the points and invent terms at fractional indices
3. 3Given versus calculated The initial value is supplied, so the table task assesses the later calculations

Given values

\(\displaystyle t_0=-3,\quad d=3\)

For t₀ = −3 and adding 3 each step, find t₁

Given values

\(\displaystyle t_1=0,\quad d=3\)

Now t₁ = 0. Find t₂ using the same rule

The table gives t₂ = 3. Which point belongs on the sequence graph?

Should the points for indices 0 and 1 be joined in a sequence graph?

Change the initial value and the additive step. Look for increasing, decreasing and constant arithmetic graphs while keeping the points separate

What happens when the additive step is zero?

For an arithmetic sequence with negative difference, the separate points:

Given values

\(\displaystyle u_0=16,\quad u_{n+1}=u_n/2\)

For u₀ = 16 and halving each step, find u₂

The exact coordinate key includes (3, 2). What does it mean?

A nonzero constant sequence has what graph?

Read precisely and draw independently

Use the exact coordinate key when a point lies between large tick intervals. A graph-choice answer shows recognition, not independent drawing

1. 1Check a candidate Compare its starting index, values and whether it joins the points
2. 2Paper construction Plot your calculated pairs on paper with labelled axes. Compare with the supplied correct graph; this drawing needs self or teacher checking