Sequences I
Q: What is the common difference of the arithmetic sequence: 4, 9, 14, 19...
A: 5
Q: A ball is dropped from a height of 10 meters and bounces back up to 80% of its previous height each time. What is the total vertical distance traveled after 5 bounces?
A: Approx. 44.26 meters
Q: Find the sum of the first 6 terms of the geometric sequence: 1, 2, 4, 8...
A: 63
Q: What is the sine of 30°?
A: ½
Q: What is the base of the exponential function f(x)=2
A: 2
Q: What is the 10th term of the arithmetic sequence: 7, 11, 15, 19...?
A: 43
Q: What is the sum of the infinite geometric series: 16 + 8 + 4 + 2 + ...
A: 32
Q: What is the 12th term of the arithmetic sequence: 3, 7, 11, 15...?
A: 47
Q: What is the cosine of 0°?
A: 1
Q: Simplify: log10(1000)
A: 3
Q: Find the sum of the first 5 terms of the arithmetic sequence: 2, 5, 8, 11...
A: 35
Q: Is the sequence 1, 3, 9, 27... arithmetic, geometric, or neither?
A: Geometric
Q: What is the sum of the first 10 terms of the geometric sequence: 2, 6, 18...?
A: 39364
Q: In a right triangle, if the opposite side is 5 and the hypotenuse is 13, what is sin(θ)?
A: 5/13
Q: Expand: log(4x^2)
A: log4+2logx
Q: Write the explicit formula for the arithmetic sequence: 10, 14, 18, 22...
A: aₙ = 10 + (n - 1)(4)
Q: What is the sum of the first 8 terms of the arithmetic sequence: 5, 8, 11...?
A: 104
Q: Is the sequence defined by aₙ = 5n² - 2 arithmetic, geometric, or neither?
A: Neither
Q: What is the tangent of 45°?
A: 1
Q: lnx = 3
A: x = e^3
Q: Write the recursive formula for the sequence: 100, 90, 81, 72.9...
A: a₁ = 100, aₙ = aₙ₋₁ × 0.9
Q: Find the number of terms in the arithmetic sequence: 4, 7, 10, ..., 64.
A: 21 terms
Q: The sum of the first 20 terms of an arithmetic sequence is 710. If a₁ = 5, what is the 20th term?
A: 66
Q: What is the value of sin(180°)?
A: 0
Q: Domain of f(x) = log(x-4)?
A: x>4