Topics › KS3 › Algebra

Sequences (nth term)

seq-01 Present from here

What is the 10th term of the sequence $3, 7, 11, 15, \ldots$?

Option A: $40$

Option B: $43$

Option C: $39$

Option D: $30$

Answer and misconceptions

Option A: $40$ ✗
Multiplies the position by the difference onlyUses 4n and forgets to adjust for the starting term: 4 × 10.

Option B: $43$ ✗
Adds the difference once for every termAdds ten lots of 4 to the first term instead of nine.

Option C: $39$ ✓ Correct

Option D: $30$ ✗
Multiplies the position by the first termThinks the 10th term is 10 × 3.
seq-02 Present from here

Which is the nth term of $5, 8, 11, 14, \ldots$?

Option A: $n + 3$

Option B: $3n + 5$

Option C: $5n + 3$

Option D: $3n + 2$

Answer and misconceptions

Option A: $n + 3$ ✗
Writes the term-to-term rule as the nth termSees "add 3" and writes n + 3.

Option B: $3n + 5$ ✗
Uses the first term as the constantAdds the 1st term instead of the zero term (5 − 3 = 2).

Option C: $5n + 3$ ✗
Swaps the roles of first term and differenceMultiplies n by the first term and adds the difference.

Option D: $3n + 2$ ✓ Correct
seq-03 Present from here

Which is the nth term of $20, 17, 14, 11, \ldots$?

Option A: $23 - 3n$

Option B: $20 - 3n$

Option C: $3n + 17$

Option D: $n - 3$

Answer and misconceptions

Option A: $23 - 3n$ ✓ Correct

Option B: $20 - 3n$ ✗
Uses the first term as the constantUses 20 instead of the zero term 20 + 3 = 23.

Option C: $3n + 17$ ✗
Ignores that the sequence is decreasingUses a difference of +3 and finds the zero term as 20 − 3.

Option D: $n - 3$ ✗
Writes the term-to-term rule as the nth termSees "subtract 3" and writes n − 3.
seq-04 Present from here

Which sequence has nth term $2n + 1$?

Option A: $1, 3, 5, 7, \ldots$

Option B: $4, 5, 6, 7, \ldots$

Option C: $2, 4, 6, 8, \ldots$

Option D: $3, 5, 7, 9, \ldots$

Answer and misconceptions

Option A: $1, 3, 5, 7, \ldots$ ✗
Starts substituting from n = 0Uses n = 0, 1, 2, 3 instead of n = 1, 2, 3, 4.

Option B: $4, 5, 6, 7, \ldots$ ✗
Reads 2n as 2 + nCalculates 2 + n + 1, so the terms go up by 1.

Option C: $2, 4, 6, 8, \ldots$ ✗
Ignores the constant termUses only 2n and forgets to add 1.

Option D: $3, 5, 7, 9, \ldots$ ✓ Correct
seq-05 Present from here

Is $40$ a term in the sequence with nth term $3n + 2$?

Option A: Yes, it is the 13th term

Option B: No, $n$ would not be a whole number

Option C: Yes, it is the 14th term

Option D: Yes, it is the 38th term

Answer and misconceptions

Option A: Yes, it is the 13th term ✗
Rounds n to the nearest whole numberSolves 3n = 38 to get 12.67 and rounds, but the 13th term is 41.

Option B: No, $n$ would not be a whole number ✓ Correct

Option C: Yes, it is the 14th term ✗
Adds the constant instead of subtracting itSolves 3n = 40 + 2 = 42, so n = 14 (but the 14th term is 44).

Option D: Yes, it is the 38th term ✗
Forgets to divide by the coefficient of nWorks out 40 − 2 = 38 and gives that as n, but the 38th term is 116.