Photo AI

Here is a sequence - OCR - GCSE Maths - Question 17 - 2020 - Paper 6

Question icon

Question 17

Here-is-a-sequence-OCR-GCSE Maths-Question 17-2020-Paper 6.png

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

Worked Solution & Example Answer:Here is a sequence - OCR - GCSE Maths - Question 17 - 2020 - Paper 6

Step 1

Work out the next term.

96%

114 rated

Answer

To find the next term in the sequence, we first observe the existing terms:

  • The first term is 3.
  • The second term is 3√5.
  • The third term is 15, which can be expressed as 3 × 5.
  • The fourth term is 15√5.

We notice a pattern:

  • The terms alternate between being a multiple of 3 and a multiple of 15, with √5 introduced in every alternate term.

Following this pattern, we conclude that the next term should be 75 (i.e., 15 × 5). Thus, the next term is 75.

Step 2

Find the nth term.

99%

104 rated

Answer

The sequence alternates between two forms:

  1. For odd n: The terms are multiples of 15. This can be expressed as:

    a_n = 15 imes 5^{(n-1)/2} ext{ for odd } n.

  2. For even n: The terms are multiples of 3 with √5. This can be expressed as:

    a_n = 3 imes 5^{n/2} ext{ for even } n.

Therefore, the overall nth term can be defined as:

an={15×5(n−1)/2if n is odd3×5n/2if n is even a_n = \begin{cases} 15 \times 5^{(n-1)/2} & \text{if } n \text{ is odd} \\ 3 \times 5^{n/2} & \text{if } n \text{ is even} \end{cases}

Join the GCSE students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;