Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Would 163 be a term in the sequence 10, 13, 16, 19, ...?

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:

13 - 10 = 3
16 - 13 = 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:

https://brainly.com/question/42554048