206, 202, 198, …
Find the 46th term.
The correct answer and explanation is:
To find the 46th term in the sequence 206, 202, 198, …, we first observe that this is an arithmetic sequence. In an arithmetic sequence, the difference between consecutive terms is constant.
Step 1: Identify the first term and common difference.
- The first term (a₁) is 206.
- To find the common difference (d), subtract the second term from the first:
d=202−206=−4d = 202 – 206 = -4.
So, the common difference is -4.
Step 2: Use the formula for the nth term of an arithmetic sequence.
The formula for the nth term of an arithmetic sequence is: an=a1+(n−1)⋅da_n = a_1 + (n – 1) \cdot d
where:
- ana_n is the nth term,
- a1a_1 is the first term,
- dd is the common difference,
- nn is the term number.
Step 3: Apply the formula to find the 46th term.
Now, substitute the known values into the formula: a46=206+(46−1)⋅(−4)a_{46} = 206 + (46 – 1) \cdot (-4)
Simplifying the expression inside the parentheses: a46=206+45⋅(−4)a_{46} = 206 + 45 \cdot (-4) a46=206−180a_{46} = 206 – 180 a46=26a_{46} = 26
Conclusion:
The 46th term in the sequence is 26. This result was obtained by applying the formula for an arithmetic sequence, using the first term, common difference, and the term number.