206, 202, 198, … Find the 46th term.
The correct answer and explanation is:
The sequence given is 206, 202, 198, …
This is an arithmetic sequence, where each term is obtained by adding or subtracting a constant value from the previous term. In this case, the common difference dd is: d=202−206=−4d = 202 – 206 = -4
Thus, the sequence decreases by 4 for each successive term. The general formula for the nn-th term of an arithmetic sequence is: an=a1+(n−1)⋅da_n = a_1 + (n – 1) \cdot d
Where:
- ana_n is the nn-th term,
- a1a_1 is the first term,
- dd is the common difference,
- nn is the term number.
We are asked to find the 46th term, so we substitute the known values into the formula: a46=206+(46−1)⋅(−4)a_{46} = 206 + (46 – 1) \cdot (-4) a46=206+45⋅(−4)a_{46} = 206 + 45 \cdot (-4) a46=206−180a_{46} = 206 – 180 a46=26a_{46} = 26
Therefore, the 46th term of the sequence is 26.
Explanation:
In this arithmetic sequence, the first term is 206, and the common difference is -4, meaning each term is 4 less than the previous one. By using the arithmetic sequence formula, we can calculate the value of any term in the sequence. In this case, to find the 46th term, we substitute the appropriate values into the formula and simplify the result to obtain 26. This method is applicable to any arithmetic sequence where the common difference and the first term are known.