Series / Sequences - Examples, Exercises and Solutions

It is possible to see that there is a difference of one number between each number.

That is, 1 is added to each number and it will be the next number:

$1+1=2$

$2+1=3$

$3+1=4$

Etcetera. Therefore, the next numbers missing in the sequence will be:$8+1=9$

$10+1=11$

To solve this problem, we'll check the differences between consecutive terms:

• The difference between $22$ and $18$ is $22 - 18 = 4$.
• The difference between $26$ and $22$ is $26 - 22 = 4$.
• The difference between $30$ and $26$ is $30 - 26 = 4$.

All differences between consecutive terms are $4$, indicating a constant increment. Thus, the sequence is arithmetic with a common difference of $4$.

The term-to-term rule is: to get the next term, add $4$ to the current term.

Therefore, yes, there is a term-to-term rule for this sequence, given by adding $4$ to the previous term.

To solve this problem, we need to determine if there's a consistent pattern or rule in the sequence $1, 2, 3, 4, 5, 6$.

Let's proceed step by step:

• Step 1: Analyze the given sequence
  The sequence is $1, 2, 3, 4, 5, 6$.
• Step 2: Check for a common difference
  Calculate the difference between each consecutive pair of numbers:

$2 - 1 = 1$
$3 - 2 = 1$
$4 - 3 = 1$
$5 - 4 = 1$
$6 - 5 = 1$

From the calculations above, we observe that the difference between each consecutive term is $+1$.

Conclusion: The sequence is an arithmetic sequence with a common difference of $+1$.

Therefore, the correct choice is $+1$.

To solve this problem, we need to analyze whether the set of numbers $10, 8, 6, 4, 2$ has a pattern or property.

• Step 1: Observe the difference between consecutive terms:
  $8 - 10 = -2$
  $6 - 8 = -2$
  $4 - 6 = -2$
  $2 - 4 = -2$
• Step 2: Analyze the result.
  We see that the difference between consecutive terms is consistently $-2$.

This indicates that the terms form an arithmetic sequence with a common difference of $-2$.

Hence, the property of this set of numbers is that it is an arithmetic sequence with a common difference of $-2$.

By comparing the possible answer choices, we confirm that the correct choice is number 1: $-2$.

One can observe that the difference between each number is 2.

That is, with each leap the next number increases by 2:

$94+2=96$

$96+2=98$

$98+2=100$

and so forth......