What is the sum of the first 10 terms of the geometric series 32 + 16 + 8 + ... ?

Here we need to use the formula for the sum of a geometric series up to n terms: s = a*(r^n-1)/(r-1). In this formula, 'a' is the first term of the series, 'r' is the common ratio between each consecutive term of the series, and 'n' is the number of terms in the series. We know n = 10, and can see that a = 32. r = 0.5, as each term in the series is half that of the previous term. We input these values into our formula to get: s = 32*(0.5^10-1)/(0.5-1). Inputting this into a calculator, we get the answer s = 63.9 (3 s.f.).

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Answered by Eleanor C. Maths tutor

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