수열 문제
등차수열과 등비수열: n번째 항과 수열의 합 구하기.
등차수열(일정한 차)과 등비수열(일정한 비)을 다루며, n번째 항과 첫 n항의 합을 구하는 방법도 포함합니다.
시작하기: 수열
수열 예제 문제
아래 예제 문제는 현재 영어로만 제공됩니다.
1. Find the 9th term of the arithmetic sequence: 4, 1, -2, -5, ...+
답: -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, ...+
답: 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, ...+
답: 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, ...+
답: 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, ...+
답: 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, ...+
답: 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.