Question

Prove that the ten’s digit of any power of 3 is even. [e.g. the ten’s digit of 3^6 = 729 is 2].

Answer 1

@TessaMarie08181997 @mikaela19900630

Answer 2

i dont get it explain more

Answer 3

[e.g. the ten’s digit of 3^6 = 729 is 2].

Answer 4

ohh i get it okay let me see

Answer 5

none of them are

Answer 6

did you try Induction proof?

Answer 7

ya I tries but was unsuccessful using it

Answer 8

\[\Large{3^1=03\quad 3^2=09\quad3^3=27\quad3^4=81\quad3^5=243\ldots\\
\text{we note that 1,3,9,7 are repeated cyclically every "4" steps of n }\\
3^n=1\,{\rm or}\,3({\rm mod}\,10)\implies3^{n+1}=3k\,({\rm mod}\,10)\\
3^n=9\,{\rm or}\,7({\rm mod}\,10)\implies3^{n+1}=3k\pm2\,({\rm mod}\,10)
}\]
we saw that
k=2 for n=2
k=8 for n=3

by induction, this will be true for all positive powers of 3

Answer 9

k = tens place digit

Answer 10

Thankyou Sir