Find the 5th term of the sequence 2,5,10,17....?

Analyze the question: We need the 5th term of the sequence 2, 5, 10, 17, ...

Find the pattern: Look at the differences between consecutive terms:

• 5 − 2 = 3
• 10 − 5 = 5
• 17 − 10 = 7

The first differences (3, 5, 7) increase by 2 each time. This is a quadratic sequence, so the next difference is 9.

Solution (Method 1: using differences):

5th term = 17 + 9 = 26

Solution (Method 2: using the nth term formula):

Compare each term with n²:

• n = 1: 1² + 1 = 2 ✓
• n = 2: 2² + 1 = 5 ✓
• n = 3: 3² + 1 = 10 ✓
• n = 4: 4² + 1 = 17 ✓

So the nth term is Tₙ = n² + 1.

T₅ = 5² + 1 = 25 + 1 = 26

Tip: When the differences between terms are not constant, check the differences of the differences. If those are constant (here, 2), the sequence is quadratic. Also, quickly compare the terms with perfect squares (1, 4, 9, 16, 25...), because many WASSCE sequences are of the form n² + k.