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The first four terms of a Fibonacci sequence are a 2a 3a 5a The sum of the first five terms of this sequence is 228 Work out the value of a. - Edexcel - GCSE Maths - Question 6 - 2021 - Paper 3

Question 6

The first four terms of a Fibonacci sequence are a 2a 3a 5a The sum of the first five terms of this sequence is 228 Work out the value of a.

Worked Solution & Example Answer:The first four terms of a Fibonacci sequence are a 2a 3a 5a The sum of the first five terms of this sequence is 228 Work out the value of a. - Edexcel - GCSE Maths - Question 6 - 2021 - Paper 3

Step 1

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Answer

To find the value of $a$ , we need to define the first five terms of the sequence. The terms can be expressed as follows:

The first term is $a$ .
The second term is $2a$ .
The third term is $3a$ .
The fourth term is $5a$ .
The fifth term can be calculated as follows:
- Since it's a Fibonacci sequence, the fifth term is the sum of the previous two terms, which is $5a + 3a = 8a$ .

Now we can sum these five terms:

$ext{Sum} = a + 2a + 3a + 5a + 8a = 19a$

Step 2

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Answer

We know from the problem statement that this sum equals 228:

$19a = 228$

To solve for $a$ , we can divide both sides by 19.

Step 3

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Answer

Dividing both sides by 19 gives us:

$a = \frac{228}{19} = 12$

Therefore, the value of $a$ is 12.

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