Find the common difference and the next term of an arithmetic sequence

The terms go from 12 to 7. What is the signed common difference?

Change the earlier term and signed change separately. Compare the later term with the next and previous terms. Try a negative change and zero

When the earlier term is 2 and the signed change is −3, what is the later term?

Keep the direction in the difference

Subtract the earlier term from the later term. The sign tells you whether the sequence rises, falls or stays constant

1. 1Forwards Add the signed difference to find the next term
2. 2Backwards Subtract the signed difference to find the previous term
3. 3Zero change A constant sequence is arithmetic with common difference zero

Given values

\(\displaystyle -7,-2\)

For consecutive terms −7 and −2, find the common difference

Given values

\(\displaystyle 8,3,-2,-7\)

The terms are 8, 3, −2, −7. Find the common difference

Given values

\(\displaystyle t=-7,\quad d=-5\)

For an arithmetic sequence with a term of −7 and common difference −5, find the next term

Given values

\(\displaystyle t=4,\quad d=-3\)

One term is 4 and the common difference is −3. Find the immediately preceding term

Why is the previous term found by subtracting the common difference?

Given values

\(\displaystyle 6,6,6,6\)

The constant sequence is 6, 6, 6, 6. Find its common difference

Given values

\(\displaystyle -1.2,-1.6,-2.0\)

For −1.2, −1.6, −2.0, write the common difference to one decimal place

Subtract the earlier term from the later term. Write a decimal with exactly one digit after the decimal point; an equivalent fraction or extra decimal place does not match this requested form

Only every second term is shown: t₀ = 4 and t₂ = 10. Is 10 − 4 the one-step common difference?

Given values

\(\displaystyle t_0=4,\quad t_2=10\)

An arithmetic sequence has t₀ = 4 and t₂ = 10. Find its one-step common difference

Check the givens and answer format

Use consecutive terms unless the number of steps is stated. Keep negative signs and any requested units or precision

1. 1Exact value Equivalent fractions and decimals are valid when no form is requested
2. 2Specified precision If one decimal place is requested, write one digit after the decimal point