Problem 19
Question
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) \(a_{20}\)
Step-by-Step Solution
Verified Answer
a) \(a_1 = 9\)
b) \(a_6 = -26\)
c) \(a_{20} = -390\)
1Step 1: 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.
2Step 2: 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.
3Step 3: 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.
Other exercises in this chapter
Problem 19
Evaluate each binomial coefficient. $$\left(\begin{array}{l}10 \\\4\end{array}\right)$$
View solution Problem 19
Find the general term, \(a_{m}\) for each geometric sequence. Then, find the indicated term. $$a_{1}=2, r=\frac{1}{5} ; a_{4}$$
View solution Problem 19
Write the first five terms of the arithmetic sequence with general term \(a_{n}\). $$a_{n}=5-n$$
View solution Problem 20
Evaluate each binomial coefficient. $$\left(\begin{array}{l}9 \\\3\end{array}\right)$$
View solution