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Chapter 15: Problem 19

Given the general term of each sequence, find each of the following. \(a_{n}=10-n^{2}\) a) the first term of the sequence b) the 6 th term c) \(a_{20}\)

Short Answer

Expert verified
a) \(a_1 = 9\) b) \(a_6 = -26\) c) \(a_{20} = -390\)

Step by step solution

01

Find the first term (a)

To find the first term of the sequence, we plug in n=1 into the general term: \(a_1 = 10 - 1^2 = 10 - 1 = 9\) So, the first term of the sequence is 9.
02

Find the sixth term (b)

To find the sixth term of the sequence, we plug in n=6 into the general term: \(a_6 = 10 - 6^2 = 10 - 36 = -26\) So, the sixth term of the sequence is -26.
03

Find the twentieth term (c)

To find the twentieth term of the sequence, we plug in n=20 into the general term: \(a_{20} = 10 - 20^2 = 10 - 400 = -390\) So, the twentieth term of the sequence is -390.

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