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A sequence {an} is defined recursively by a1 = 2, a2 = 4 and an = an1 + 2an1 for n

Chapter 4, Problem 20

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QUESTION:

A sequence {an} is defined recursively by a1 = 2, a2 = 4 and an = an1 + 2an1 for n 3.Prove that an = 2n for every positive integer n.

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QUESTION:

A sequence {an} is defined recursively by a1 = 2, a2 = 4 and an = an1 + 2an1 for n 3.Prove that an = 2n for every positive integer n.

ANSWER:

Problem 20

A sequence  is defined recursively by  and  for .

Prove that  for every positive integer .

                                                        Step by Step Solution

Step 1 of 4

Consider the given statement,

 

Check for  as,

Thus, it is observed that  is true.

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