This question tests upper-level ISEE quantitative reasoning skills, specifically determining missing terms in sequences. Sequences follow specific patterns, such as arithmetic or geometric, where each term depends on the previous term(s) based on a set rule. In this sequence, 1, 4, 9, _, 25, the pattern involves perfect squares: 1²=1, 2²=4, 3²=9, 4²=16, 5²=25. Choice C (16) is correct because it equals 4², following the identified pattern of consecutive perfect squares, showing understanding of quadratic sequences. Choice B (14) is incorrect because it assumes a different pattern, perhaps thinking the differences increase linearly rather than recognizing the square number pattern. To help students: Memorize common sequences like perfect squares (1, 4, 9, 16, 25, 36...), look for patterns in both the terms and their positions, and recognize that some sequences are based on mathematical operations applied to the term's position number.

This question tests upper-level ISEE quantitative reasoning skills, specifically determining missing terms in sequences. Sequences follow specific patterns, such as arithmetic or geometric, where each term depends on the previous term(s) based on a set rule. In this sequence, 3, 6, 12, _, 48, the pattern involves multiplying each term by 2 to get the next term (3×2=6, 6×2=12, 12×2=24, 24×2=48). Choice D (24) is correct because it follows the identified geometric pattern of doubling, showing understanding of multiplicative sequences. Choice C (22) is incorrect because it assumes an arithmetic pattern rather than geometric, a common error when students don't test whether differences or ratios are constant. To help students: Always check both differences and ratios between terms, practice recognizing geometric sequences where each term is multiplied by the same factor, and verify the pattern works for all given terms.

This question tests upper-level ISEE quantitative reasoning skills, specifically determining missing terms in sequences. Sequences follow specific patterns, such as arithmetic or geometric, where each term depends on the previous term(s) based on a set rule. In this fundraiser sequence, 120, 150, _, 210, 240, the pattern involves adding 30 to each term to get the next term (120+30=150, 150+30=180, 180+30=210, 210+30=240). Choice C (180) is correct because it follows the identified arithmetic pattern of adding 30, showing understanding of constant growth in real-world contexts. Choice B (170) is incorrect because it assumes a different increment, perhaps thinking the increase is 20 rather than 30, a common error when not carefully calculating differences. To help students: Connect sequences to real-world scenarios like fundraising to make patterns more meaningful, always calculate differences between known consecutive terms, and verify patterns work for all given values before selecting an answer.

This question tests upper-level ISEE quantitative reasoning skills, specifically determining missing terms in sequences. Sequences follow specific patterns, such as arithmetic or geometric, where each term depends on the previous term(s) based on a set rule. In this sequence with the rule multiply by 3: 2, 6, _, 54, 162, each term is multiplied by 3 to get the next term (2×3=6, 6×3=18, 18×3=54, 54×3=162). Choice B (18) is correct because it follows the given geometric pattern of multiplying by 3, showing understanding of applying stated rules to sequences. Choice C (20) is incorrect because it doesn't follow the multiply-by-3 rule, perhaps resulting from adding rather than multiplying or misunderstanding the pattern. To help students: When a rule is explicitly given, apply it consistently to each term, verify by checking that the rule produces all given terms, and practice with both arithmetic and geometric sequences to distinguish between additive and multiplicative patterns.

This question tests upper-level ISEE quantitative reasoning skills, specifically determining missing terms in sequences. Sequences follow specific patterns, such as arithmetic or geometric, where each term depends on the previous term(s) based on a set rule. In this sequence, 2, 3, 5, _, 13, the pattern involves adding consecutive terms to get the next term (2+3=5, 3+5=8, 5+8=13), which is the Fibonacci pattern. Choice B (8) is correct because it follows the identified pattern of adding the two previous terms, showing understanding of recursive sequences. Choice C (9) is incorrect because it assumes a different pattern, perhaps thinking the differences increase by 1 each time, missing the Fibonacci relationship. To help students: Look for patterns involving relationships between multiple terms, practice recognizing famous sequences like Fibonacci, and always verify the pattern by checking if it produces all given terms correctly.

This question tests upper-level ISEE quantitative reasoning skills, specifically determining missing terms in sequences. Sequences follow specific patterns, such as arithmetic or geometric, where each term depends on the previous term(s) based on a set rule. In this sequence, 81, 27, _, 3, 1, the pattern involves dividing each term by 3 to get the next term (81÷3=27, 27÷3=9, 9÷3=3, 3÷3=1). Choice D (9) is correct because it follows the identified geometric pattern of dividing by 3, showing understanding of decreasing geometric sequences. Choice C (8) is incorrect because it doesn't maintain the consistent ratio of 1/3 between consecutive terms, perhaps resulting from a calculation error or misidentifying the pattern. To help students: Recognize that geometric sequences can involve division (multiplication by fractions), practice with both increasing and decreasing geometric sequences, and always verify the pattern by checking ratios between all consecutive terms.

This question tests upper-level ISEE quantitative reasoning skills, specifically determining missing terms in sequences. Sequences follow specific patterns, such as arithmetic or geometric, where each term depends on the previous term(s) based on a set rule. In this sequence, 14, 18, _, 26, 30, the pattern involves adding 4 to each term to get the next term (14+4=18, 18+4=22, 22+4=26, 26+4=30). Choice C (22) is correct because it follows the identified pattern of adding 4, showing understanding of arithmetic sequences. Choice B (21) is incorrect because it assumes an inconsistent pattern, perhaps thinking the differences vary, which is a common error for students not recognizing constant differences. To help students: Practice identifying differences between consecutive terms, use number lines to visualize equal spacing in arithmetic sequences, and always verify patterns by checking multiple terms in the sequence.