Here are the first four terms of a sequence - OCR - GCSE Maths - Question 4 - 2019 - Paper 1

I analyzed the first four terms of the sequence and calculated the differences between them. Noticing that each term increases by 5, I established that the common difference is 5. I then applied this pattern to find the next term by adding 5 to the last term, 18, resulting in 23.

The sequence identified is an arithmetic sequence where each term increases by a constant value of 5. The general formula for the $n^{th}$ term of the sequence can be expressed as:

$T_n = 3 + (n-1) imes 5$

For 534 to be a term in this sequence, we would set $T_n = 534$ and rearrange the formula:

$534 = 3 + (n-1) imes 5$

Subtract 3 from both sides:

$531 = (n-1) imes 5$

Divide both sides by 5:

n - 1 = rac{531}{5} = 106.2

This result indicates that $n$ would not be a whole number, meaning that 534 cannot be achieved through integer values of $n$. Therefore, 534 is not a term in the sequence.