A formula for a typical term of a sequence or an expansion in terms of its index: aₙ as a formula in n for a sequence, C(n, r) aⁿ⁻ʳ bʳ for a binomial expansion.
例文
話し言葉 Write down the (r + 1)th term first, then choose r so the power of x is 4. まず第 r + 1 項(一般項)を書いて、x の次数が 4 になるように r を決める。
書き言葉・答案 Find the general term of the geometric sequence 5, 20, 80, 320, … 等比数列 5, 20, 80, 320, … の一般項を求めよ。
言い間違えやすいところ
数列の一般項 aₙ は、OpenStax Algebra and Trigonometry(13.1)・Intermediate Algebra(12.1)でも general term (nth term)。n の式そのものは explicit formula(漸化式の recursive formula と対。エントリ find-the-nth-term)とも呼ぶ。
二項定理の展開式の一般項 ₙCᵣ aⁿ⁻ʳ bʳ を、OpenStax Algebra and Trigonometry(Binomial Theorem)は the (r+1)th term of the binomial expansion、OpenStax Intermediate Algebra(Binomial Theorem)は the (r + 1)st term と書き、general term とは呼ばない。
用例コーパスの書き言葉は OpenStax Intermediate Algebra が中心で、次が OpenStax Algebra and Trigonometry(数列と級数)。
Khan Academy Algebra / Khan Academy AP Calculus / Khan Academy AP Statistics / Khan Academy Middle School (6th-8th Grade, Pre-Algebra) / MIT OCW 18.01 Single Variable Calculus / MIT OCW 18.03 Differential Equations / MIT OCW 18.06 Linear Algebra / Professor Leonard
取得元(書き言葉)
OpenStax Algebra and Trigonometry 2e / OpenStax Calculus Vol 1-3 / OpenStax Intermediate Algebra 2e / OpenStax Introductory Statistics 2e