The kth term of a sequence is $r^k$, where $r \neq 0$ - OCR - GCSE Maths - Question 17 - 2023 - Paper 6
Question 17
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=r2
The sixth term is given by:
a6=r6
According to the problem, we have:
a6=3imesa2.
Step 2
Set up the equation
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Answer
Substituting the expressions for the terms, we obtain:
r6=3r2.
Step 3
Solve for r
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Answer
To solve for r, divide both sides by r2 (noting that r=0):
r4=3
Taking the fourth root, we find:
r=31/4=43.
Calculating this gives:
r≈1.316.
Step 4
Round to three decimal places
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Answer
Finally, rounding r to three decimal places, we get:
r≈1.316.
