# List the first 10 terms of each of these sequences

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Practice problem 20

List the first 10 terms of each of these sequences.

a) The sequence whose nth term is the larges integer k such that k! <= n;

b) The sequence whose nth term is 3^n - 2^n;

c) The sequence whose nth term is sqrt(n) ;

d) The sequence whose nth term is the sum of the first n positive integers

e) The sequence obtained by starting with 10 and obtaining each term by subtracting 3 from the previous term

f) The sequence whose nth term is the largest integer whose binary expansion has n bits

g) The sequence whose first two terms are 1 and 2 and each succeeding term is the sum of the two previous terms

h) The sequence whose terms are constructed sequentially as follows: start with 1, then add 1, then multiply by 1, then add 2, then multiply by 2 and so on

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#### Solution Preview

Practice problem 20

List the first 10 terms of each of these sequences.

a) The sequence whose nth term is the larges integer k such that

When n = 1, , then k = 0 or 1. so the larger one is k = 1.

When n = 2, , then k = 0, 1, or 2, so the largest one is k = 2.

When n = 3, , then k= 0, 1, or 2, so the largest one is k= 2.

When n= 4, , then k = 0, 1, or 2, so the larges one is k = 2.

When n= 5, , then k = 0, 1, or 2, so the larges one is k = 2.

When n= 6, , then k = 0, 1, 2, or 3, so the larges one is k = 3.

When n= 7, , then k = 0, 1, 2, or 3, so the larges one is k = 3.

When n= 8, , then k = 0, 1, 2, or 3, so the larges one is k = 3.

When n= 9, , then k = 0, 1, 2, or 3, so the larges one is k = 3.

When n= 10, , then k = 0, 1, 2, or 3, so the larges one is k = 3.

Here

Therefore, the first 10 terms of the sequences are: 1, 2, 2, 2, 2, 3, 3, 3, 3, 3.

b) The sequence whose nth term is

The first 10 terms are: 1, 5, 19, 65, 211, 665, 2059, 6305, 19171, 58025

c) The ...

#### Solution Summary

It lists the first 10 terms of each of these sequences. The solution is detialed and well presented.