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DNA sequences in animals can be written as a sequence of letters. One section of DNA is made up of the letters CTAGCGT repeated over and over, as shown below. a) What is the 7^th letter in the DNA sequence? b) What is the 14^th letter in the DNA sequence? c) What is the 700^th letter in the DNA sequence? Write a sentence to explain your method.

Question

DNA sequences in animals can be written as a sequence of letters.
One section of DNA is made up of the letters CTAGCGT repeated
over and over, as shown below.
a) What is the 7^th letter in the DNA sequence?
b) What is the 14^th letter in the DNA sequence?
c) What is the 700^th letter in the DNA sequence?
Write a sentence to explain your method.

DNA sequences in animals can be written as a sequence of letters. One section of DNA is made up of the letters CTAGCGT repeated over and over, as shown below. a) What is the 7^th letter in the DNA sequence? b) What is the 14^th letter in the DNA sequence? c) What is the 700^th letter in the DNA sequence? Write a sentence to explain your method.

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BerniceMaster · Tutor for 5 years

Answer

For position 7, using the formula established:<br />\[7 \mod 7 = 0\]<br />Hence, the \(7^{th}\) letter is 'T'.<br /><br />For position 14th, <br />\[14 \mod 7 = 0\]<br />So, the 14th letter is also 'T' in the sequence.<br /><br />For position 700th, <br />\[700 \mod 7 = 0\]<br />Thus, the 700th letter in the sequence is also 'T'. <br /><br />In conclusion, for any position that gives a remainder of 0 when divided by 7, the letter at that position in the recurring sequence is 'T'. This is because each pattern of ‘CTAGCGT’udes 7 letters, so concluding it to be n letters divided by 7 with no remainder covers all positions occupied by 'T'.

Explain

## Step 1:<br />We are given that the pattern recurring in the DNA sequence is "CTAGCGT". This pattern consists of seven letters. For positions that are multiples of seven, the last letter "T" would appear.<br /><br />## Step 2:<br />To identify the letter at any given position, given that the pattern is comprised of seven letters, we perform a modulus operation by 7 on the given position. If the answer to this operation is "0", it means the position is multiple of seven, and hence the last letter "T" would appear at that position.<br /><br />## Step 3:<br />Applying the rule from Step 2, the remainder when the sought position divided by 7 determines the letter's position in the recurring sequence CTAGCGT. And we can thus identify the-letter for each position by mapping the modulus result to the sequence position.
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