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Solving a Quadratic Equation by Factorization Method

For what valu...

Question

For what value of n, 2ⁿ ✕ 5ⁿ ends in 5.

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Solution

We need to find the value of n, for which ends in 5.

Clearly,

Also, all the values of n will make end in 0.

Thus, there is no value of n for which ends in 5.

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Similar questions

Show that there is no value of n for which ( $2^{n} \times 5^{n}$ ) ends in 5.

If $2^{n - 7} \times 5^{n - 4} = 1250$ find the value of $n$ .

For what value of n, 5ⁿ ends with a zero

Q. If the ratio of sum of first

n

terms of two A.P.s is

2 n + 8 : 5 n - 3,

then the ratio of

n^{th}

terms of those two A.P.s is

Q. If n is any natural number, then 6ⁿ − 5ⁿ always ends with

(a) 1
(b) 3
(c) 5
(d) 7

[Hint: For any n ∈ N, 6ⁿ and 5ⁿ end with 6 and 5 respectively. Therefore, 6ⁿ − 5ⁿ always ends with 6 − 5 = 1.]

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