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