Answer :

Final answer:

The number 163 is a term in the arithmetic sequence 10, 13, 16, 19,... because it is the 52nd term in the sequence. This sequence has a common difference of 3. The formula for the n-th term confirms this result.


Explanation:

Determining if 163 is a Term in the Sequence

The sequence given is: 10, 13, 16, 19.... This is an arithmetic sequence where each term increases by a constant difference. To find the common difference, we can subtract the first term from the second:

  1. 13 - 10 = 3
  2. 16 - 13 = 3
  3. 19 - 16 = 3

The common difference in this sequence is 3.

We can represent the n-th term of an arithmetic sequence using the formula:

a_n = a_1 + (n - 1) d

where:

  • a_n = n-th term
  • a_1 = first term (10 in this case)
  • d = common difference (3)
  • n = term number

Substituting the known values into the formula gives:

a_n = 10 + (n - 1) 3

Now, to determine if 163 is a term in the sequence, we need to set a_n = 163 and solve for n:

163 = 10 + (n - 1) 3

Subtracting 10 from both sides:

153 = (n - 1) 3

Now divide both sides by 3:

51 = n - 1

Add 1 to both sides:

n = 52

This indicates that 163 is indeed the 52nd term in the sequence. Therefore, the answer is:

Yes, 163 is a term in the sequence.


Learn more about Arithmetic Sequence here:

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