3^0 3^1 3^2 3^3 3^4 3^5
1 3 9 27 81 243
If the series of numbers continues, what is the digit in the unit column for 3^10? Please explain.

Question

3^0	3^1	3^2	3^3	3^4	3^5
1	3	9	27	81	243
If the series of numbers continues, what is the digit in the unit column for 3^10? Please explain.

anonymous · Answer

3

anonymous · Answer

no its 9.

anonymous · Answer

it is geometric progression, with commun ration =3. Notice that the next term is equal the previous one multiplied by 3

anonymous · Answer

huh?

anonymous · Answer

so just keep multiplying till get to 10º term

jim_thompson5910 · Answer

Notice the pattern of units digits: 1, 3, 9, 7, 1, 3, 9, 7...

anonymous · Answer

yes 9..

anonymous · Answer

3^0	3^1	3^2	3^3	3^4	3^5      3^5        3^5
1	3	9	27	81	243      243*3    243*3*3

anonymous · Answer

where did you get the 7?

jim_thompson5910 · Answer

It repeats every 4 terms, so because 10/4 = 2 remainder 2, this means that the units digit for 3^10 is the same as the units digit for 3^2

anonymous · Answer

I dont understand how you got  the 7?

jim_thompson5910 · Answer

3^3 = 27, so that's how we got that units digit

anonymous · Answer

doesnt make sense though, where you got the 7?

anonymous · Answer

3^0	3^1	3^2	3^3
1               3               9               27

27*3         27*(3*3)       27*(3*3*3)   27*(3*3*3*3)
81	243            729           2187

notice that the last digits are always 1,3,9,7

anonymous · Answer

oh okay, thank you!!