1 Consider the table:

1= 1

2+3+4=1+8

5+6+7+8+9= 8+27

10+11+12+13+14+15+16=27 +64

Guess the general law suggested by these examples, express it in suitable mathematical notation, and prove it.

2. Three numbers are in arithmetic progression, three other numbers in geometric progression. Adding the corresponding terms of these two progressions successively, we obtain

85, 76, and 84

respectively, and adding all three terms of the arithmetic pro- gression, we obtain 126. Find the terms of both progressions.

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