GCSE OCR Maths Surds: Here is a sequence. 5 5√3

Here is a sequence - OCR - GCSE Maths - Question 16 - 2018 - Paper 5

Question 16

Here is a sequence. 5 5√3 15 15√3 (a) Work out the next term. (b) Find the nth term.

Worked Solution & Example Answer:Here is a sequence - OCR - GCSE Maths - Question 16 - 2018 - Paper 5

Step 1

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Answer

To determine the next term in the sequence, let's examine the terms given:

Observing the sequence, we notice that the numbers alternate between a multiple of 5 and a multiple of √3. The pattern seems to be as follows:

Following the pattern, the next term (5th term) would be $5 \times 5 = 25$ .

Step 2

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Answer

To find the nth term of the sequence, we can deduce a general formula based on the identified pattern.

The terms can be represented as follows:

For odd n, the terms are: $5 \times (n/2)$ when n is odd (1st, 3rd, ...)
For even n, the terms are: $5 \times (n/2) \sqrt{3}$ when n is even (2nd, 4th, ...)

Thus, we can express the nth term as:

$T(n) = 5 \times \left(\left(\frac{n+1}{2}\right) \text{ for odd n, and } \left(\frac{n}{2}\right) \sqrt{3} \text{ for even n}\right)$

This captures the required format for the nth term.