Math Problem Statement
How to read it all in a sentence Step 1: Identify the first term (a1a1)
The first term of the sequence is given as 1661.
Step 2: Determine the common difference (dd)
The common difference dd is found by subtracting the first term from the second term. For this sequence:
d=13−16=26−16=16d=31−61=62−61=61
Verify by subtracting the second term from the third term:
12−13=36−26=1621−31=63−62=61
So, d=16d=61.
Step 3: Use the formula for the nth term
The formula for the nnth term of an arithmetic sequence is:
an=a1+(n−1)×dan=a1+(n−1)×d
Here, we want to find the 5th term (a5a5).
Step 4: Substitute the values
Substitute a1=16a1=61, d=16d=61, and n=5n=5 into the formula:
a5=16+(5−1)×16a5=61+(5−1)×61a5=16+4×16a5=61+4×61a5=16+46=1+46=56a5=61+64=61+4=65
Step 5: Conclude the answer
The 5th term of the sequence is 5665.
Solution
To summarize the process in one sentence:
To find the 5th term of the arithmetic sequence where the first term is and the common difference , you use the formula , and after substituting , , and , the 5th term is calculated as .
Would you like further details or have any questions?
Here are 5 related questions to expand on this:
- How do you find the sum of the first terms of an arithmetic sequence?
- What happens to the common difference if the sequence is geometric instead of arithmetic?
- How do you determine if a sequence is arithmetic or geometric?
- How would you find the 100th term of this sequence?
- What is the formula for the nth term of a geometric sequence?
Tip: Always verify your common difference by subtracting consecutive terms; this ensures that the sequence is indeed arithmetic.
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Math Problem Analysis
Mathematical Concepts
Arithmetic Sequences
Formulas
Formula for the nth term of an arithmetic sequence: $a_n = a_1 + (n - 1) \times d$
Theorems
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Suitable Grade Level
High School
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