Question

the first three terms of a sequence are given. write your answer as a decimal or whole number. round to the nearest thousandth (if necessary).

3, 12, 21, ...

find the 43rd term.

Explanation:

Step1: Identify sequence type

Check difference between terms: \(12 - 3 = 9\), \(21 - 12 = 9\). It's an arithmetic sequence with \(a_1 = 3\), \(d = 9\).

Step2: Use arithmetic sequence formula

The formula for the \(n\)-th term of an arithmetic sequence is \(a_n = a_1 + (n - 1)d\). Substitute \(a_1 = 3\), \(d = 9\), \(n = 43\):
\(a_{43} = 3 + (43 - 1) \times 9\)

Step3: Calculate the value

First, \(43 - 1 = 42\). Then, \(42 \times 9 = 378\). Finally, \(3 + 378 = 381\).

Answer:

381