Answer:
2500
Step-by-step explanation:
it is a geometric progression
r=5
The geometric sequence 4, 20, 100, 500 is [tex]\rm a_n = 4 \times 5^{n-1}[/tex].
A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant.
This ratio is known as a common ratio of the geometric sequence.
The given geometric sequence 4, 20, 100, 500.
The common difference between the geometric sequence is;
[tex]\rm \dfrac{a_2}{a_1}=\dfrac{20}{4} =5\\\\ \dfrac{a_3}{a_2}=\dfrac{100}{20} =5\\\\ \dfrac{a_4}{a_3}=\dfrac{500}{100} =5\\\\[/tex]
The formula geometric sequence is;
[tex]\rm a_n = a_1 \times r^{n-1}\\\\ a_n = 4 \times 5^{n-1}[/tex]
Where a1 is the first term and r is the common difference of the given geometric sequence.
Hence, the geometric sequence 4, 20, 100, and 500 is [tex]\rm a_n = 4 \times 5^{n-1}[/tex].
Learn more about geometric sequence here;
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