Arithmetic Sequence (AP)
Q: If the sum of the first n terms of an arithmetic sequence is given by \(S_n = 3n^2 + 2n\), find the common difference
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Step 1: Calculate the numerator: \(4.5 \times 3.2 = 14.4\). Step 2: Divide by the denominator: \(\frac{14.4}{1.8} = 8.0\). Step 3: Apply significant figures. For multiplication and division, the answer should have the same number of significant figures as the number with the FEWEST significant figures in the calculation. All three numbers (4.5, 3.2, and 1.8) have 2 significant figures, so our answer must have 2 s.f. The result 8.0 already has 2 significant figures (the 8 and the 0 after the decimal point, which is significant). Therefore, the answer is 8.0. Note: Writing just '8' would only show 1 s.f., so we must write 8.0 to show 2 s.f. This distinction is critical in ECZ marking schemes.
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