等差数列の計算機（第 n 項と和）
この計算機は、毎回同じ数だけ増える（または減る）数列の第 n 項と、初項から第 n 項までの和を求めます。初項、公差、n を入力してください。
結果
値を入力して「計算」を押すと結果が表示されます。
公式
Start at the first term and add the difference n − 1 times.
The sum is the number of terms times the average of the first and last term.
この計算ツールの使い方
- Enter the first term and the common difference (the amount added each time; negative if the sequence goes down).
- Enter n, the term you want (and how many terms to add).
- Press Calculate to see the nth term, the sum and the first few terms.
解き方付き例題
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.
よくある間違い
- 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.
よくある質問
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 + …).