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The kth term of a sequence is $r^k$, where $r \neq 0$ - OCR - GCSE Maths - Question 17 - 2023 - Paper 6

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The kth term of a sequence is $r^k$, where $r \neq 0$. The sixth term is equal to three times the second term. Find the value of $r$, giving your answer correct ... show full transcript

Worked Solution & Example Answer:The kth term of a sequence is $r^k$, where $r \neq 0$ - OCR - GCSE Maths - Question 17 - 2023 - Paper 6

Step 1

Express the terms

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Answer

The second term of the sequence is given by: a2=r2a_2 = r^2 The sixth term is given by: a6=r6a_6 = r^6 According to the problem, we have: a6=3imesa2a_6 = 3 imes a_2.

Step 2

Set up the equation

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Answer

Substituting the expressions for the terms, we obtain: r6=3r2r^6 = 3r^2.

Step 3

Solve for r

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Answer

To solve for rr, divide both sides by r2r^2 (noting that r≠0r \neq 0): r4=3r^4 = 3 Taking the fourth root, we find: r=31/4=34.r = 3^{1/4} = \sqrt[4]{3}. Calculating this gives: r≈1.316.r \approx 1.316.

Step 4

Round to three decimal places

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Answer

Finally, rounding rr to three decimal places, we get: r≈1.316.r \approx 1.316.

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