Find term n of an arithmetic sequence using the rule

Starting from t₀, how many updates lead to t₄?

Keep the start at 2 and the difference at 3. Move the index from 0 to 6. Then change the difference to a negative value or zero and compare the total change

At start 2, difference 3 and index 4, what is the term?

Count the updates

When the first supplied value has index zero, index n means n equal updates

1. 1Explicit rule Add n copies of the signed difference to the initial value \(\displaystyle t_n=t_0+nd\)
2. 2Recurrence rule A recurrence uses the previous term; an explicit rule uses the index directly

Given values

\(\displaystyle t_0=7,\quad d=4\)

For t₀ = 7 and difference 4, find the constant term in tₙ = A + Bn

Given values

\(\displaystyle t_0=7,\quad d=4\)

For the same sequence, find the coefficient B in tₙ = A + Bn

For t₀ = 7 and common difference 4, which explicit rule applies?

Given values

\(\displaystyle t_n=7+4n\)

Use that explicit rule to find t₂₀

Given values

\(\displaystyle u_0=18,\quad d=-3\)

For u₀ = 18 and difference −3, find u₅

Given values

\(\displaystyle u_0=18,\quad d=-3\)

For the same sequence, find u₈

If the first supplied term is t₁ instead of t₀, how many updates reach tₙ?

Given values

\(\displaystyle t_1=5,\quad d=2\)

An arithmetic sequence has t₁ = 5 and difference 2. Find t₄

Given values

\(\displaystyle t_0=6,\quad t_5=26\)

An arithmetic sequence has t₀ = 6 and t₅ = 26. Find its difference

Given values

\(\displaystyle d=-2,\quad t_4=9\)

An arithmetic sequence has difference −2 and t₄ = 9. Find t₀

Construct and check your rule

On paper, write a complete explicit rule from an initial value and a difference. Check it at the initial index and at the next index

1. 1Check the indexing Use t₀ + nd for a zero-index start, or t₁ + (n − 1)d for a one-index start
2. 2What the activities show Coefficient entry and choice questions check parts of rule construction. An independently written rule still needs self or teacher checking