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A sequence is defined by the rule $u_{n+1} = 5 u_n - 15.$ (a) If $u_3 = 6$, calculate (i) $u_5$ - OCR - GCSE Maths - Question 13 - 2019 - Paper 1

Question 13

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A sequence is defined by the rule $u_{n+1} = 5 u_n - 15.$ (a) If $u_3 = 6$, calculate (i) $u_5$

Worked Solution & Example Answer:A sequence is defined by the rule $u_{n+1} = 5 u_n - 15.$ (a) If $u_3 = 6$, calculate (i) $u_5$ - OCR - GCSE Maths - Question 13 - 2019 - Paper 1

Step 1

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Answer

To find $u_4$ , we use the recurrence relation:

$u_4 = 5 u_3 - 15$

Substituting in the value of $u_3$ :

$u_4 = 5(6) - 15 = 30 - 15 = 15$

Step 2

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Answer

Next, to find $u_5$ , we again use the recurrence relation:

$u_5 = 5 u_4 - 15$

Substituting in the value of $u_4$ :

$u_5 = 5(15) - 15 = 75 - 15 = 60$

Thus, the value of $u_5$ is 60.

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