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The cost of determining a person’s complete genetic blueprint is about to plummet again — to $5,000.

That is the price that a start-up company called Complete Genomics says it will start charging next year for determining the sequence of the genetic code that makes up the DNA in one set of human chromosomes. The company is set to announce its plans on Monday.

Such a price would represent another step toward the long-sought goal of the “$1,000 genome.” At that price point it might become commonplace for people to obtain their entire DNA sequences, giving them information on what diseases they might be predisposed to or what drugs would work best for them.

“It’s a shockingly low price,” said George M. Church, a professor of genetics at Harvard who is an adviser to Complete Genomics and to several other sequencing companies.

Then again, the cost of DNA sequencing has dropped by a factor of 10 every year for the last four years, a faster rate of decline than even for computers, Dr. Church said.

DNA consists of a string...