Final answer:
An explicit formula for the arithmetic sequence is an = 3 + (n-1)4, and the tenth term is 39. For the fractional sequence, the explicit formula is an = 1/(n+1), resulting in the tenth term being 1/11.
Step-by-step explanation:
To write an explicit formula for each sequence and find the tenth term, we must identify the pattern in each sequence:
a. Arithmetic Sequence
The given sequence 3, 7, 11, 15, 19, ... is an arithmetic sequence, where each term increases by a common difference of 4. An arithmetic sequence can be expressed as an = a1 + (n-1)d, where an is the nth term, a1 is the first term, d is the common difference, and n is the term number. Using this formula, the explicit formula for this sequence is an = 3 + (n-1)4. To find the tenth term, a10 = 3 + (10-1)4 = 3 + 36 = 39.
b. Fraction Sequence
The second sequence 1/2, 1/3, 1/4, 1/5, 1/6, ... is a sequence where the denominator of each fraction increases by 1. This pattern gives us the formula an = 1/(n+1). Therefore, the tenth term is a10 = 1/(10 + 1) = 1/11.