Sequence is actually the range of a function having for its domain the set of positive integers or a subset of it. If all of the positive integers comprise the domain, then the sequence is infinite; otherwise, it is finite. Also, sequence is a particular order in which related events, movements, or things follow each other.
• Arithmetic Sequence – is a sequence of numbers such that the difference of any two successive members of the sequence is a constant.
• Geometric Sequence – is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
• Harmonic Sequence – is a sequence of real numbers formed by taking the reciprocals of an arithmetic progression. Equivalently, it is a sequence of real numbers such that any term in the sequence is the harmonic mean of its two neighbors.
• Fibonacci Numbers – commonly denoted as F_n form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from 0 to 1.
Formula of Geometric Sequence: a_n = a_1 r^(n-1)
Definition of terms:
a_n – last term of the sequence or unknown sequence
a_1 – first term of the sequence
r – common ratio
n – number of terms or sequence
Solution:
1. Determine the given of the problem.
a_n – unknown sequence
a_1 – 3/20
r – ((3⁄2)/(3⁄20)) = 10
n – 5
2. Substitute the given to the formula of the geometric sequence.
a_n = a_1 r^(n-1)
a_5 = (3/20) (10)^(5-1)
3. Solve the given problem.
a_5 = (3/20) (10)^(5-1) - Subtract the exponent.
a_5 = (3/20) (10)^(4) - Multiply 1/10 to the exponent.
a_5 = (3/20)(10000) - Multiply it.
a_5 = (30000/20) - Divide it.
a_5 = 1,500 - Answer of the problem.
Answer: The 5th term of the Geometric Sequence 3/20, 3/2, 15, … is 1,500.
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