数列 問題
等差数列と等比数列：第n項と数列の和を求める。
等差数列（一定の差）と等比数列（一定の比）をカバーし、第n項の求め方と最初のn項の和の求め方を含みます。
はじめる： 数列
数列の例題
以下の例題は現在、英語のみで提供されています。
1. Find the 9th term of the arithmetic sequence: 4, 1, -2, -5, ...+
答え: -20
Step 1: Find the common difference: 1 - 4 = -3. Step 2: Use the nth-term formula: a_n = a_1 + (n - 1)d = 4 + (9 - 1)(-3). Step 3: a_9 = 4 + -24 = -20.
2. Find the 5th term of the geometric sequence: 2, 4, 8, 16, ...+
答え: 32
Step 1: Find the common ratio: 4 / 2 = 2. Step 2: Use the nth-term formula: a_n = a_1 × r^(n - 1) = 2 × 2^4. Step 3: a_5 = 2 × 16 = 32.
3. Find the 14th term of the arithmetic sequence: -1, 4, 9, 14, ...+
答え: 64
Step 1: Find the common difference: 4 - -1 = 5. Step 2: Use the nth-term formula: a_n = a_1 + (n - 1)d = -1 + (14 - 1)(5). Step 3: a_14 = -1 + 65 = 64.
4. Find the 12th term of the arithmetic sequence: -1, 5, 11, 17, ...+
答え: 65
Step 1: Find the common difference: 5 - -1 = 6. Step 2: Use the nth-term formula: a_n = a_1 + (n - 1)d = -1 + (12 - 1)(6). Step 3: a_12 = -1 + 66 = 65.
5. Find the 5th term of the geometric sequence: 5, 15, 45, 135, ...+
答え: 405
Step 1: Find the common ratio: 15 / 5 = 3. Step 2: Use the nth-term formula: a_n = a_1 × r^(n - 1) = 5 × 3^4. Step 3: a_5 = 5 × 81 = 405.
6. Find the 4th term of the geometric sequence: 1, 2, 4, 8, ...+
答え: 8
Step 1: Find the common ratio: 2 / 1 = 2. Step 2: Use the nth-term formula: a_n = a_1 × r^(n - 1) = 1 × 2^3. Step 3: a_4 = 1 × 8 = 8.