Arithmetic Series Sum - Precalculus & Trigonometry Step by Step

Sum the first n terms of an arithmetic sequence using S_n = n/2 · (a_1 + a_n), where a_n is the nth term.

Example

Use the arithmetic series formula to find a finite sum.

highlighted = computed this step

Step 1 — Set up

Set up the expression.

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

Step 2 — Last term

Find the tenth term: 39.

a_{ 10 }= \hl{39}

Step 3 — Sum formula

Use the arithmetic series sum formula.

S_n=\frac{n}{ 2 }(a_{ 1 }+a_n)

Step 4 — Substitute

Substitute n = 10, first term 3, and last term 39.

S_{ 10 }=\frac{ \hl{10} }{ 2 }( \hl{3} + \hl{39} )

Step 5 — Result

The sum of the first 10 terms is 210.

S_{ 10 }= \hl{210}

arithmetic-series-sum The sum of the first n terms of an arithmetic sequence: S_n = n/2 · (a_1 + a_n) Steps: 1. Find a_n using a_n = a_1 + (n-1)d. 2. Apply the sum formula with the known a_1 and a_n. 3. Simplify: n/2 · (a_1 + a_n).