Problem 18
Find the nth term of the arithmetic sequence \(\left\\{a_{n}\right\\}\) whose first term \(a_{1}\) and common difference d are given. What is the 51st term? $$ a_{1}=-2 ; \quad d=4 $$
Problem 18
Show that each sequence is geometric. Then find the common ratio and list the first four terms. $$ \left\\{u_{n}\right\\}=\left\\{\frac{2^{n}}{3^{n-1}}\right\\} $$
Problem 19
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers \(n\). $$ n^{2}+n \text { is divisible by } 2 $$
Problem 19
Find the nth term of the arithmetic sequence \(\left\\{a_{n}\right\\}\) whose first term \(a_{1}\) and common difference d are given. What is the 51st term? $$ a_{1}=8 ; \quad d=-7 $$
Problem 19
List the first five terms of each sequence. \(\left\\{c_{n}\right\\}=\left\\{(-1)^{n+1} n^{2}\right\\}\)
Problem 19
Expand each expression using the Binomial Theorem. $$ (x-2)^{6} $$
Problem 19
Find the fifth term and the nth term of the geometric sequence whose first term \(a_{1}\) and common ratio \(r\) are given. $$ a_{1}=2 ; \quad r=3 $$
Problem 20
Expand each expression using the Binomial Theorem. $$ (x+3)^{5} $$
Problem 20
Find the nth term of the arithmetic sequence \(\left\\{a_{n}\right\\}\) whose first term \(a_{1}\) and common difference d are given. What is the 51st term? $$ a_{1}=6 ; \quad d=-2 $$
Problem 20
List the first five terms of each sequence. \(\left\\{d_{n}\right\\}=\left\\{(-1)^{n-1}\left(\frac{n}{2 n-1}\right)\right\\}\)
