Algebra 4th edition ch.5 Problem Set

[Marleny.santos]

I think there is an error on the Problem Set of the Algebra book (guide 1) of the 4th edition. On page 124, problem #17 reads:

An = 2n - 1 for all integers n>1 (greater than or equal)

Quantity A : units digit of A26
Quantity B : units digit of A34

The solution given is that they are equal, but I do not understand why as

A26= 2(26)-1= 52-1= 51
B34= 2(34)-1= 68-1=67

1<7

The explanation given is that powers of 2 have repeating patterns of four terms for units digits (2,4,8,6) HOWEVER, it could alsoend in 0 so there are five terms, not four.

Anyways, I just wanted to know i there is amistake or I am completely missing it...

Thanks

[tommywallach]

Hey Marleny,

Hmm. You seem to have copied this down wrong, the question says:

Asubn = 2^n - 1 for all integers n> 1

Quantity A : units digit of A26
Quantity B : units digit of A34

So you're not multiplying 2 by 26. You're raising it to the 26th power. And when raising 2 to a power, it couldn't end in zero:

2 ^ 1 = 2
2 ^ 2 = 4
2 ^ 3 = 8
2 ^ 4 = 16
2 ^ 5 = 32
2 ^ 6 = 64
etc.

See? The pattern is repeating every 4 terms. so following this pattern, 2^2 ends in a 4, and so will 2^6, 2^10, 2^14, 2^18, 2^22, 2^26, 2^30, and 2^34.

That means the answer will be (C).

[Monnk13]

The answer given is for 2^n-1 but the actual question reads 2n-1 (one less than the product of 2n instead of 2 to the power of n minus 1)

[tommywallach]

Hey Monk/Marleny,

My apologies! I was looking at the 3rd edition, which has the same question on the same page, without an error. But you're absolutely right. I'll have it added to errata.

-t