IGCSE Mathematics (0580)

Sequences

What this topic tests, the mistakes that cost marks, and one exam-style question worked through step by step.

Key ideas and common mistakes

Correctly substitute the given term number into the nth term formula, ensuring the exponent is applied before multiplication.
Common mistake: Students often multiply before squaring, e.g., calculating 2 × 3 then squaring, instead of squaring 3 first.
To find a specific term in a sequence given by a formula, substitute the correct value of n (here, n = 2 for the second term).
Common mistake: A common mistake is to substitute n = 1 or misapply the formula.
To find missing terms at the start or end of an arithmetic sequence, use the common difference and move backward or forward accordingly.
Common mistake: A common mistake is to subtract instead of add when moving to an earlier term, or vice versa.
Identify a geometric sequence by checking for a constant ratio between terms, not a constant difference.
Common mistake: Students who look for an arithmetic pattern may incorrectly add the previous difference instead of multiplying by the common ratio.
For geometric sequences where the first term is not 1, the nth term is a × r^(n-1) with the correct exponent.
Common mistake: Students often use n-1 without adjusting for the actual first term's exponent, so their formula gives the wrong starting value.
The first term of a sequence defined by nth term formula is found by substituting n = 1, not n = 0.

The nth term of a sequence is 2n^2 + 5. Find the third term of this sequence.

Try it first, then show the working

Substitute n = 3 into 2n^2 + 5.
2 x 3^2 + 5 = 2 x 9 + 5 = 18 + 5 = 23.
Check by listing the first terms: n = 1 gives 7, n = 2 gives 13, n = 3 gives 23.

Answer: 23

18 exam-style questions on Sequences, each marked to the scheme.