Write explicitly the terms of an arithmetic sequence of length 6 with first term a = 1.5 and common difference d = 0.7.
Understand the Problem
The question is asking to explicitly write the terms of an arithmetic sequence given the first term and common difference. Specifically, it requires calculating and listing the sequence terms based on the formula for an arithmetic sequence.
Answer
The arithmetic sequence
Answer for screen readers
The arithmetic sequence is: $1.5, 2.2, 2.9, 3.6, 4.3, 5.0$
Steps to Solve
- Identify the first term and common difference
Given the first term $a = 1.5$ and the common difference $d = 0.7$, we will start with the first term and use the common difference to find the subsequent terms.
- Calculate the second term
To find the second term $b_2$, add the common difference to the first term:
$$ b_2 = a + d = 1.5 + 0.7 = 2.2 $$
- Calculate the third term
To find the third term $b_3$, add the common difference to the second term:
$$ b_3 = b_2 + d = 2.2 + 0.7 = 2.9 $$
- Calculate the fourth term
To find the fourth term $b_4$, add the common difference to the third term:
$$ b_4 = b_3 + d = 2.9 + 0.7 = 3.6 $$
- Calculate the fifth term
To find the fifth term $b_5$, add the common difference to the fourth term:
$$ b_5 = b_4 + d = 3.6 + 0.7 = 4.3 $$
- Calculate the sixth term
To find the sixth term $b_6$, add the common difference to the fifth term:
$$ b_6 = b_5 + d = 4.3 + 0.7 = 5.0 $$
- List the terms of the sequence
The arithmetic sequence of length 6 is:
$$ b_1, b_2, b_3, b_4, b_5, b_6 = 1.5, 2.2, 2.9, 3.6, 4.3, 5.0 $$
The arithmetic sequence is: $1.5, 2.2, 2.9, 3.6, 4.3, 5.0$
More Information
This arithmetic sequence starts at $1.5$ and increases by $0.7$ for each term, producing a sequence of values that can be useful in various mathematical contexts, such as financial calculations or computer science algorithms.
Tips
- Adding the common difference incorrectly; be sure to always add $d$ to the most recent term.
- Forgetting to include all terms up to the specified length, which in this case is 6.
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