Answer:
2. 2n+1
3. n+3
4. see below for "reasoning"
Step-by-step explanation:
2.a. Stays the same: one light square; two columns of dark squares.
Changes: the number of dark squares in a column.
2.b. The number of dark squares in a column is equal to the figure number, so the total number of squares is two times the figure number, plus one.
2.c. 2n+1
2.d. coefficient: 2; constant: 1
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3.a. (figure, triangles) = (1, 4), (2, 5), (3, 6), (4, 7), (5, 8)
3.b. The number of triangles is 3 more than the figure number.
3.c. n+3
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4.a. Seemingly, Anne is counting the number of squares above the corner (n), the corner square (1), and the number of squares to the right of the corner (n), for a total of n + 1 + n.
4.b. It appears that Sanjay is counting the number of squares above the bottom row (n) and the number in the bottom row (n+1), for a total of n + (n+1).
4.c. However Robert counts it, he realizes the simplified form of the expression can be 2n+1.
