Question

check whether 15n can end with the digit 6 (six) for any n and N .and give reason.
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Answer 1

It cannot cause your question is invalid

Answer 2

Given :   15n  or 15ⁿ  n ∈ N

To Find : check whether 15n or 15ⁿ  can end with the digit 6 (six)  

Solution:

case 1 : 15n

15n

= 15 x n

= 3 x 5 x n

Any integer number multiplied by 5  always ends with 5 or 0

Hence 15n  can not end with the digit 6 (six)  

case 1 : 15ⁿ

15ⁿ  for n = 0  its 1

for rest

15ⁿ   = ( 3 x 5)ⁿ

= 5 * 3ⁿ * 5ⁿ⁻¹

3ⁿ * 5ⁿ⁻¹ is an integer

Any integer number multiplied by 5  always ends with 5 or 0

Hence 15ⁿ  can not end with the digit 6 (six)  

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