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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:
Tn = a + (n - 1)d
= 4 + (n - 1)(5)
= 4 + (n - 1)(5)
= 4 + 5n - 5
= 5n - 1
The nth term is explicitly given as Tn = 5n - 1
Summary:
The explicit form of the pattern: 4, 9, 14, 19, … is Tn = 5n - 1