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). 10, 15, 20, ... find the 39th term.

Explanation:

Step1: Identify the sequence type

This is an arithmetic sequence where the first term \(a_1 = 10\) and the common difference \(d = 15 - 10 = 5\) (or \(20 - 15 = 5\)).

Step2: Use the arithmetic sequence formula

The formula for the \(n\)-th term of an arithmetic sequence is \(a_n = a_1 + (n - 1)d\).

Step3: Substitute values for the 39th term

We need to find \(a_{39}\), so \(n = 39\), \(a_1 = 10\), and \(d = 5\).
Substitute into the formula: \(a_{39} = 10 + (39 - 1) \times 5\)

Step4: Calculate the value

First, calculate \(39 - 1 = 38\).
Then, \(38 \times 5 = 190\).
Finally, \(10 + 190 = 200\).

Answer:

200