Question

Prove that the sum of two consecutive exponents of the number 5 is divisible by 30.If two consecutive exponents are 5n and 5n + 1, then their sum can be written as _· 30.

Answer 1

Answer:

$5^{n-1}*30$

Step-by-step explanation:

Here you mean :

$5^n+5^{n+1}=$

So we can simplify this expression and we have :

$5^n+5^n*5=$

We need to find common factor :

$5^n(1+5)$

So we have :

$5^n*6$

Now, we need to think how can write 5^n on different way. Maybe to try add 1 and subtract 1 from exponent :

$5^{n+1-1}*6=5^{n-1}*5*6=\\5^{n-1}*30$

Answer 2

Hence Proved that the sum of two consecutive exponents of the number 5 is divisible by 30. and if two consecutive exponents are $5^n$ and $5^{n+1}$, then their sum can be written as $5^{n-1} * 30$.

What is exponents?

Exponentiation is a mathematical operation, written as aⁿ.

Let suppose two consecutive exponents of 5 are :

$5^{n} \text{ and }5^{n+1}$

Sum of these exponents is

$5^{n}+5^{n+1}$

So we writes this expression as

$5^{n}+5^{n} * 5=$

$5^{n}(1+5)$

$5^{n} * 6$

=$5^{n-1} * 30$

So it will be divisible by 30 .

Hence Proved that the sum of two consecutive exponents of the number 5 is divisible by 30. and if two consecutive exponents are $5^n$ and $5^{n+1}$, then their sum can be written as $5^{n-1} * 30$.

To learn more about exponents visit

https://brainly.com/question/847241