Math Quiz - Sequences Report a question What's wrong with this question? You cannot submit an empty report. Please add some details. Math Quiz - Sequences Covering: arithmetic and geometric sequences, partial sums, and recursive formulas, as well as real-world applications of sequence concepts. 1 / 5 1. For a geometric sequence, given the first term a₁ = 3 and the common ratio r = 2, what is the 5th term of the sequence? a) 36 b) 60 c) 48 d) 24 To compute any term in a geometric sequence, we can use the formula: aₙ = a₁ * r^(n - 1) We are given: a₁ = 3, r = 2, and we need to find the 5th term, so n = 5. Plugging in the values: a₅ = 3 * 2^(5 - 1) a₅ = 3 * 2^4 a₅ = 3 * 16 a₅ = 48 So, the 5th term of the geometric sequence is 48. The correct answer is 48. 2 / 5 2. Given an arithmetic sequence with a first term of a₁ = 2 and a common difference of d = 2, what is the 6th term of the sequence? a) 12 b) 14 c) 16 d) 18 To find the 6th term of the arithmetic sequence, we can use the formula: aₙ = a₁ + (n-1)d We are given: a₁ = 2, d = 2, and n = 6. Plugging in the values: a₆ = 2 + (6-1)(2) a₆ = 2 + 10 a₆ = 12 So, the 6th term of the arithmetic sequence is 12. The correct answer is 12. 3 / 5 3. If the first three terms of an arithmetic sequence are 3, 5, and 7, what is the common difference d? a) 1 b) 2 c) 3 d) 4 To find the common difference (d), we can subtract the first term from the second term, or the second term from the third term: d = 5 - 3 = 2 d = 7 - 5 = 2 So, the common difference d is 2. The correct answer is 2. 4 / 5 4. In a geometric sequence, if the first term is a₁ = 8 and the common ratio r = -2, what is the 4th term of the sequence? a) -16 b) -32 c) -64 d) 64 To find the 4th term of the geometric sequence, we can use the formula: aₙ = a₁ * r^(n-1) We are given: a₁ = 8, r = -2, and n = 4. Plugging in the values: a₄ = 8 * (-2)^(4-1) a₄ = 8 * (-2)^3 a₄ = 8 * -8 a₄ = -64 So, the 4th term of the geometric sequence is -64. The correct answer is) -64. 5 / 5 5. In a geometric sequence, the first term a₁ = 4, and the common ratio r = 3. What is the sum of the first 6 terms? a) 1456 b) 800 c) 1200 d) 2000 To find the sum of the first 6 terms of a geometric sequence, we can use the formula: Sₙ = a₁ * (1 - r^n) / (1 - r) We are given: a₁ = 4, r = 3, and n = 6. Plugging in the values: S₆ = 4 * (1 - 3^6) / (1 - 3) S₆ = 4 * (1 - 729) / (-2) S₆ = 4 * 728 / 2 S₆ = 4 * 364 So, the sum of the first 6 terms of this geometric sequence is 1456. The correct answer is) 1456. Your score is 0% Restart Quiz