ExplanationThis is a geometric sequence: each new number is created by multiplying the previous number by 2.

Calculate the first few terms of the series to find the pattern: 1, 2, 4, 8, 16, and so on.

Geometric sequences can be written in this form: \(a_n = r^{n – 1}\), where r is the multiplied constant and n is the number of the desired term. In this case, the function is \(a_n = 2^{n – 1}\).

The question asks for the difference between the sum of the first 10 terms and the sum of the 11th and 12th terms. While there is a clever pattern at play, it is hard to spot. If you don’t see the pattern, one way to solve is to use the calculator to add the first ten terms: 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 = 1,023.

The 11th term plus the 12th term is equal to 1,024 + 2,048 = 3,072. Subtract 1,023 to get 2,049.

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Sandy

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