What is the general term of the sequence 3, 8, 13, 18, ...?

Analyze the question: The sequence 3, 8, 13, 18, ... increases by the same amount each time, so it is an arithmetic progression (AP). We need a formula for the nth term.

Concept: For an AP, the nth term is

Tₙ = a + (n − 1)d

where a is the first term and d is the common difference.

Solution:

• First term: a = 3
• Common difference: d = 8 − 3 = 5 (check: 13 − 8 = 5, 18 − 13 = 5)

Substitute into the formula:

Tₙ = 3 + (n − 1)(5) Tₙ = 3 + 5n − 5 Tₙ = 5n − 2

Check by substituting values:

• n = 1: 5(1) − 2 = 3 ✓
• n = 2: 5(2) − 2 = 8 ✓
• n = 3: 5(3) − 2 = 13 ✓
• n = 4: 5(4) − 2 = 18 ✓

Now the other options:

• B (5n + 2) gives 7 for n = 1, which is wrong.
• C (5) is just the common difference, not the general term.
• D (5n) gives 5 for n = 1, which is wrong.

5n − 2**.

Exam tip: When you are stuck on "general term" questions, plug n = 1 and n = 2 into each option. Only the correct one will give the first two terms. This takes under 20 seconds. Also remember that the coefficient of n is always the common difference, so here it must be 5, and the constant is a − d = 3 − 5 = −2.