Sequences and Series

Arithmetic Sequences

Find the nth term of an arithmetic sequence using a_n = a_1 + (n-1)d, where d is the common difference.

Example

Use the arithmetic sequence formula to find a term.

highlighted = computed this step

Step 1 — Set up

Set up the expression.

a1=3d=4n=10a_{ 1 }= 3 \quad d= 4 \quad n= 10

Step 2 — Formula

Use the arithmetic sequence formula.

an=a1+(n−1)da_n=a_{ 1 }+(n- 1 )d

Step 3 — Substitute

Substitute n = 10, first term 3, and difference 4.

a10=3+(10−1)⋅4a_{ 10 }= \hl{3} +( \hl{10} - 1 )\cdot \hl{4}

Step 4 — Result

The tenth term is 39.

a10=39a_{ 10 }= \hl{39}
arithmetic-sequence An arithmetic sequence has a constant difference d between consecutive terms: a_{n+1} - a_n = d for all n. The nth term formula: a_n = a_1 + (n-1)d. - a_1 is the first term - d is the common difference - n is the term number