요금제

등차수열 계산기 (일반항과 합)

이 계산기는 매번 같은 수만큼 커지거나 작아지는 수열의 제n항과 첫째항부터 제n항까지의 합을 구합니다. 첫째항, 공차, n을 입력하세요.

결과

값을 입력하고 계산을 누르면 결과가 표시됩니다.

공식

an=a1+(n−1)da_n = a_1 + (n - 1)d

Start at the first term and add the difference n − 1 times.

Sn=n2(a1+an)S_n = \frac{n}{2}(a_1 + a_n)

The sum is the number of terms times the average of the first and last term.

이 계산기 사용법

  1. Enter the first term and the common difference (the amount added each time; negative if the sequence goes down).
  2. Enter n, the term you want (and how many terms to add).
  3. Press Calculate to see the nth term, the sum and the first few terms.

풀이 예제

3, 7, 11, 15, … : the 10th term and the sum of 10 terms

a₁₀ = 3 + 9 × 4 = 39.

S₁₀ = 10/2 × (3 + 39) = 5 × 42 = 210.

A decreasing sequence: 20, 17, 14, …

a₈ = 20 + 7 × (−3) = −1.

S₈ = 8/2 × (20 + (−1)) = 4 × 19 = 76.

The sum 1 + 2 + … + 100

a₁₀₀ = 100, so S₁₀₀ = 100/2 × (1 + 100) = 5050.

자주 하는 실수

  • Using n instead of n − 1 in the nth-term formula: the first term already counts as one.
  • Getting the sign of d wrong for a decreasing sequence.
  • Adding the terms with the sum formula but the wrong last term.

자주 묻는 질문

How do you find the nth term of an arithmetic sequence?

Use aₙ = a₁ + (n − 1)d. For 3, 7, 11, …: a₁ = 3 and d = 4, so aₙ = 3 + 4(n − 1) = 4n − 1.

How do you find the common difference?

Subtract any term from the next one: 7 − 3 = 4. It is the same for every pair in an arithmetic sequence.

What is the difference between an arithmetic sequence and series?

A sequence is the list of terms (3, 7, 11, …); a series is their sum (3 + 7 + 11 + …).