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Chapter 8: Problem 5

Write the first six terms of each arithmetic sequence. $$a_{1}=300, d=-90$$

Short Answer

Expert verified
The first six terms of the arithmetic sequence are 300, 210, 120, 30, -60, and -150.

Step by step solution

01

Identify first term and common difference

From the given information, we know that the first term \(a_{1}\) of the sequence is 300 and the common difference \(d\) is -90.
02

Determine the second term

Apply the formula for the nth term of an arithmetic sequence. This gives us \(a_{2} = a_{1} + (2 - 1) * d = 300 + (1 * -90) = 210\).
03

Determine the third term

Again, apply the formula, which gives us \(a_{3} = a_{1} + (3 - 1) * d = 300 + (2 * -90) = 120\).
04

Determine the fourth term

Apply the formula to get \(a_{4} = a_{1} + (4 - 1) * d = 300 + (3 * -90) = 30\).
05

Determine the fifth term

Using the formula, we get \(a_{5} = a_{1} + (5 - 1) * d = 300 + (4 * -90) = -60\).
06

Determine the sixth term

Finally, apply the formula to get \(a_{6} = a_{1} + (6 - 1) * d = 300 + (5 * -90) = -150\).

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