A sequence begins like this: $\newline$ $3, 11, 19, \dots$ $\newline$ Each term is $8$ more than the previous term. Which three of the following numbers do not belong in the sequence?

Full solution

Q. A sequence begins like this:

\newline

3, 11, 19, \dots

\newline

Each term is

8

more than the previous term. Which three of the following numbers do not belong in the sequence?

Determine Pattern: Determine the pattern of the sequence. $\newline$ The sequence starts with $3$ and each term is $8$ more than the previous term. This indicates that the sequence is arithmetic with a common difference of $8$ .
Calculate Next Terms: Calculate the next few terms in the sequence to establish a pattern. $\newline$ Starting with $3$ , the next term is $3 + 8 = 11$ , and the term after that is $11 + 8 = 19$ . Continuing this pattern, we can find the next few terms: $\newline$ $19 + 8 = 27$ $\newline$ $27 + 8 = 35$ $\newline$ $35 + 8 = 43$
List Sequence Terms: List out the terms of the sequence to identify which numbers do not belong. $\newline$ The sequence so far is: $3, 11, 19, 27, 35, 43$ . Any number that cannot be obtained by starting with $3$ and repeatedly adding $8$ does not belong in the sequence.
Compare with Options: Compare the given options with the sequence to find the numbers that do not belong. Without the options provided, we cannot complete this step. However, any number that is not of the form $3 + 8n$ (where $n$ is a non-negative integer) does not belong in the sequence.