What is the remainder when 3^1+3^2+ is divided by 8.

4

Step-by-step explanation:

To find:

The remainder, when 3^0 + 3^1 + 3^2 + ... +3^2009 is divided by 8

Approach and Working:

Rem (3^0/8) = 1

Rem (3^1/8) = 3

Rem (3^2/8) = 1

Rem (3^3/8) = 3

Rem (3^4/8) = 1

Rem (3^5/8) = 3 and so on…

We can observe that,

For even powers of 3, the remainder is 1

And for odd powers of 3, the remainder is 3.

Therefore, we can rewrite the given series, in terms of its remainders, as

= 1 + 3 + 1 + 3 + 1 + 3 + … + 3 = 1005 pairs of (1 + 3) = 1005 x 4 = 4020

Rem (4020/8) = 4

the first one

step-by-step explanation:

just id the test.

the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner is 2.

spinner 1 spinner 2

1                     1

1                     2

1                     3

1                     4

2                   1

2                   2

2                   3

2                   4   = not 1, and 4

3                   1

3                   2

3                   3

3                   4 = not 1, and 4

only 2 outcomes have passed the given condition.

step-by-step explanation: