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What is the 5th term of the geometric sequence 3/20, 3/2, 15,...?

Sagot :

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Answer: What is the 5th term of the geometric sequence 3/20, 3/2, 15,...?

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.  

Kinds of a Sequence:  

• 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.

For more information just click the link below :

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