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. Find the general term of the sequence 1, 1000, 10 000 000, 1 000 000 000 000 000,...

2 Answers

7 votes

Final answer:

The general term of the given sequence is 10 to the power of 3 times the term number (
10^(3n)) starting from n=0. This sequence showcases the use of powers of ten, which is fundamental in expressing numbers in scientific notation.

Step-by-step explanation:

The given sequence is 1, 1,000, 10,000,000, 1,000,000,000,000,000,... This sequence can be described using powers of ten. On close observation, we can notice that the exponents of 10 increase in a particular pattern. The first term has 10 to the power of 0 (10^0), which is 1, the second term is 10^3 which equals 1,000, the third term is 10^6 for 10,000,000, and so on. The pattern is that the exponent increases by 3 with each term. Hence, the general term of the sequence can be expressed as
10^(3n), where n is the term number starting from 0, 1, 2, ...

To verify, we can substitute the term numbers:

  • n=0: 10^3(0) = 100 = 1
  • n=1: 10^3(1) = 103 = 1,000
  • n=2: 10^3(2) = 106 = 10,000,000


This confirms our formula for the general term.

User Dominic Cronin
by
7.6k points
1 vote
1000(n-1) would be the general term, I think...
User GMD
by
7.8k points

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