The following pattern starts with 8 and uses the rule to add 13 to the previous term. 8, 21, 34, 47, 60, ... Which of the following statements are true about the eighth term of the... The following pattern starts with 8 and uses the rule to add 13 to the previous term. 8, 21, 34, 47, 60, ... Which of the following statements are true about the eighth term of the pattern? Choose 2 answers: (Choice A) It is greater than 100. (Choice B) It is an odd number. (Choice C) It is a multiple of 9.
Understand the Problem
The question is asking us to find the eighth term in a numerical pattern that starts with 8 and adds 13 for each subsequent term. Once we find the eighth term, we need to evaluate which of the provided statements about it are true. This involves calculating the eighth term and checking its properties.
Answer
$99$
Answer for screen readers
The eighth term of the sequence is $99$.
Steps to Solve
- Identify the Sequence Formula
In a sequence where we start with a number and add a constant to get the next term, we can express the $n$-th term as: $$ a_n = a_1 + (n - 1)d $$ where $a_1$ is the first term, $d$ is the common difference, and $n$ is the term number.
In this case, we have:
- $a_1 = 8$
- $d = 13$
- Plug in the Values to Find the 8th Term
We want to find the eighth term, so we let $n = 8$: $$ a_8 = 8 + (8 - 1) \cdot 13 $$
- Calculate the Expression
Now simplify the expression: $$ a_8 = 8 + 7 \cdot 13 $$ Calculate $7 \cdot 13$: $$ 7 \cdot 13 = 91 $$ Now add 8: $$ a_8 = 8 + 91 = 99 $$
The eighth term of the sequence is 99.
The eighth term of the sequence is $99$.
More Information
The sequence in question is an arithmetic sequence, where a constant value (the common difference) is added to each term to get the next term. This kind of sequence is very common in mathematics and appears in various real-life applications, such as calculating interest or planning budgets.
Tips
- Miscalculating the product when computing $d(n - 1)$. Always double-check multiplication.
- Forgetting to add the first term (8 in this case) after calculating the product. Make sure to include it to get the correct term.
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