# State the explicit form of the pattern: 4, 9, 14, 19, …

**Solution:**

The pattern 4, 9, 14, 19, … is an arithmetic progression with first term a = 4 and difference 5 (9 - 4 = 5; 14 - 9 = 5)

The nth term of the series is defined as:

T_{n} = a + (n - 1)d

= 4 + (n - 1)(5)

= 4 + (n - 1)(5)

= 4 + 5n - 5

= 5n - 1

The nth term is explicitly given as T_{n} = 5n - 1

## State the explicit form of the pattern: 4, 9, 14, 19, …

**Summary:**

The explicit form of the pattern: 4, 9, 14, 19, … is T_{n} = 5n - 1

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