5^n+1+4.6^n whwn divide by 20 leaves remainder 9 prove by mathematical induction

It is true for all values if n

Step-by-step explanation:

Let

We have to prove that 20 is a factor of P(n) by mathematical induction.

Let us start:

Step1:

Check P(n) is true for 1.

Hence P(n) is true for n=1

Step 2:

Assume that P(n) is true for some value of n say t

That is P(t) is true or

Where k is some constant…

Step3:

We have to prove that P(t+1) is also true, then P(n) is true for every value of n.

Hence

where r is some constant.

Hence

is also true ,

Thus P(n) is true for all values of n , and we can say that

When is divided by 20, we get 9 as remainder.

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