If an arithmetic sequence has a first term of 2 and a common difference of 3, what is the fifth term?
Understand the Problem
The question is asking us to find the fifth term of an arithmetic sequence where the first term is 2 and the common difference is 3. To solve this, we will use the formula for the nth term of an arithmetic sequence, which is given by: 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.
Answer
The fifth term is $14$.
Answer for screen readers
The fifth term of the arithmetic sequence is $14$.
Steps to Solve
- Identify the given values
We know the following from the problem:
- First term ($a_1$) = 2
- Common difference ($d$) = 3
- We need to find the fifth term ($n=5$).
- Substitute the values into the formula
Using the formula for the nth term of an arithmetic sequence: $$ a_n = a_1 + (n - 1) * d $$
Substituting the known values: $$ a_5 = 2 + (5 - 1) * 3 $$
- Calculate the expression
Now simplify the expression: $$ a_5 = 2 + 4 * 3 $$
Calculate the multiplication: $$ a_5 = 2 + 12 $$
- Find the final value of the fifth term
Now sum up the values: $$ a_5 = 14 $$
The fifth term of the arithmetic sequence is $14$.
More Information
Arithmetic sequences have a constant difference between consecutive terms. In this case, each term after the first is increased by 3, starting from 2. Hence, the fifth term can be found easily using the formula for arithmetic sequences.
Tips
- Forgetting to subtract 1 from $n$ in the formula. It's important to properly calculate $(n - 1)$ to get the right index for the term.
- Confusing the common difference with the term's position in the sequence.
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