Find the 168th term of the arithmetic sequence \(\{a_{n}, n = 1, 2, 3, \ldots\}\) with common difference \(d = 1.5\) and first term \(a_{1} = 2\).
Answer (2)
a 1 = 2 ; d = 1.5 a n = a 1 + ( n − 1 ) d a n = 2 + ( n − 1 ) ⋅ 1.5 = 2 + 1.5 n − 1.5 = 0.5 + 1.5 n a 168 = 0.5 + 1.5 ⋅ 168 = 0.5 + 252 = 252.5
The 168th term of the arithmetic sequence is 252.5, calculated using the formula for the nth term with the given first term and common difference. By substituting the values into the formula, we arrive at this result. This demonstrates how to find a term in an arithmetic sequence step-by-step.
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