Answer:
Step-by-step explanation:
To prove: The sum of two consecutive exponents of the number 6 is divisible by 7.
Proof: Let the consecutive exponents of the number 6 be:
[tex]6^{n}[/tex] and [tex]6^{n+1}[/tex].
Then , the sum of two consecutive exponents of the number 6 is represented as :
[tex]6^{n}+6^{n+1}[/tex].
Now, according to question, we have to prove that The sum of two consecutive exponents of the number 6 is divisible by 7, thus
[tex]6^{n}+6^{n+1} =6^{n}+6^{n}{\times}6[/tex]
=[tex]6^{n}(1+6)[/tex]
⇒[tex]6^{n}+6^{n+1}[/tex]=[tex]6^{n}(7)[/tex]
which means that the sum of two consecutive exponents of the number 6 is divisible by 7.
Hence proved.
