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Chapter 12: Q. 7 (page 816)

In the problem, show that each sequence is arithmetic. Find the common difference and write out the first four terms.

an=2n-5

Short Answer

Expert verified

The solution is d=2; first four terms=-3,-1,1,3.

Step by step solution

01

Step 1. Given information 

an=2n-5

02

Step 2. Calculation 

The first term is a1=2路1-5=-3.

The nth term and the n-1st term of the sequence are-

an=2n-5 and an-1=2n-1-5=2n-2-5=2n-7

The common difference is -

d=an-an-1=2n-5-2n-7=2

Since the difference of any two successive terms is the constant 2, the sequence anis arithmetic.

The first four terms are-3,-1,1,3.

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Most popular questions from this chapter

In Problems 17鈥�28, write down the first five terms of each sequence.

an=nn+2

In Problems 51鈥�60, write out each sum.

鈭�k=2n-1kInk

In Problems 37鈥�50, a sequence is defined recursively. Write down the first five terms.

a1=2;an=-an-1

In Problems 51鈥�66, determine whether each infinite geometric series converges or diverges. If it converges, find its sum.

鈭�k=1鈭�332k-1

Fibonacci Sequence: Let

un=(1+5)n-(1-5)n2n5

define the nth term of a sequence.

(a) Show that u1= 1 and u2 = 1.

(b) Show that un+2 = un+1 + un.

(c) Draw the conclusion that {un} is the Fibonacci sequence.
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