iGCSE Mathematics (0580) : C2.7 Continue a given number sequence. iGCSE Style Questions Paper 1

The given sequence is an arithmetic sequence where each term is obtained by adding a constant difference of 4 to the previous term.
So, the next term in the sequence would be:
\(17 + 4 = 21\)
Therefore, the next term in the sequence is 21.

The given sequence is a geometric sequence where each term is obtained by multiplying the previous term by a constant ratio of 2.
So, the next term in the sequence would be:
\(24 \times 2 = 48\)
Therefore, the next term in the sequence is 48.

The given sequence is an arithmetic sequence where each term is obtained by adding a constant difference of 5 to the previous term.
To find an expression for the nth term of this sequence, we can use the formula for the nth term of an arithmetic sequence:
\(a_n = a_1 + (n – 1) \cdot d\)
Where:
\(a_n\) is the nth term of the sequence.
\(a_1\) is the first term of the sequence.
\(n\) is the term number.
\(d\) is the common difference between consecutive terms.
In this case, the first term \(a_1\) is 2 and the common difference \(d\) is 5.
Substitute the values into the formula:
\(a_n = 2 + (n – 1) \cdot 5\)
\(a_n = 2 + 5n – 5\)
\(a_n = 5n – 3\)
Therefore, the expression for the nth term of the given sequence is \(5n – 3\).