Number Series and Unit Conversions

This series follows an alternating pattern: multiply by 2, then subtract 8. The pattern is: 14×2=28, 28-8=20, 20×2=40, 40-8=32, 32×2=64. Following this pattern, the next operation is 64-8=56. The two-step pattern (multiply, subtract) repeats consistently.

The series follows a repeating subtraction pattern of -2, then -4. Specifically: 36-2=34, 34-4=30, 30-2=28, 28-4=24. Following this logic, the next step is 24-2, which equals 22.

The series follows an alternating pattern of subtracting 1 and adding 2. Starting from 22: 22-1=21, 21+2=23, 23-1=22, 22+2=24, 24-1=23, so the next step is 23+2=25.

The pattern alternates: odd-positioned terms are squared (1²=1 stays, 3²=9), even-positioned terms are doubled (2×2=4, 4×2=8). So the 7th term (odd position) is 4²=16. The sequence follows two different rules for odd and even positions.

This sequence is perfect cubes: 1³=1, 2³=8, 3³=27, 4³=64, 5³=125, so 6³=216. Each term is the cube of its position in the sequence (n³). This is a classic number series pattern.

The pattern is +2, +3, +4, +5 (each increment increases by 1). So the next increment is +6: 24 + 6 = 30.

The pattern is -7 each time: 63-56=7, 56-49=7, 49-42=7. So 42-7=35.

The pattern is -7 each time: 63-56=7, 56-49=7, 49-42=7. So 42-7=35.

An Astronomical Unit (AU) is defined as the average distance between the Earth and the Sun, approximately 149,597,870.691 kilometers. This is a standard unit of measurement used in astronomy for distances within the solar system. The other values are close approximations but not the precise accepted value.

One light-year is the distance light travels in one year in vacuum, which is approximately 9.46 × 10^12 kilometers. This is a standard astronomical unit for measuring interstellar distances. The other values (9.47, 9.48, 9.50) are close approximations but not the precise accepted value.

One mile equals approximately 1.61 kilometers (more precisely, 1.60934 km). This is the standard international conversion for the mile to the metric system. The other values (1.57, 1.60, 1.59) are not the accepted conversion factors.

One parsec equals approximately 3.08572 × 10^13 kilometers (about 3.26 light-years). A parsec is defined as the distance at which one astronomical unit subtends an angle of one arcsecond. The other values are close but not the precise accepted measurement.

One hectometer equals 0.1 kilometer, since 'hecto' means 100 and a hectometer is 100 meters, while a kilometer is 1000 meters. The prefix 'hecto-' in the metric system denotes a factor of 100. The other options (10 km, 100 km, 1000 km) are incorrect conversions.

This series consists of perfect squares of numbers increasing by 5: 1² = 1, 5² = 25, 10² = 100, 15² = 225, 20² = 400. The missing term is 10² = 100. The other options (75, 125, 200) are not perfect squares.

The pattern multiplies by consecutive integers starting from 2: 4 × 2 = 8, 8 × 3 = 24, 24 × 4 = 96, 96 × 5 = 480, so 480 × 6 = 2880. This is a factorial-like progression without factorial growth. Options B and C have incorrect digits, while D is too small.

This is an alternating series with two interleaved patterns: odd positions (3, 4, 5, 6, ...) increase by 1, even positions (10, 9, 8, ...) decrease by 1. After 5 comes 8 (the next even-position term). Options A, C, D don't fit this pattern.

The pattern multiplies each term by 4: 5 × 4 = 20, 20 × 4 = 80, 80 × 4 = 320, 320 × 4 = 1280, so 1280 × 4 = 5120. This is a geometric progression with common ratio 4. Options A, B, C are incorrect calculations.