Question

For any integral value of n, 7³ⁿ + 14n + 24 when divided by 7 will leave the remainder.

1. 4
2. 3
3. 5
4. 2

Answer 1

Correct Answer - Option 2 : 3

Given:

7³ⁿ + 14n + 24 divided by 7

Concept used:

Number = Divisor × Dividend + Remainder

Calculation:

7³ⁿ + 14n + 24 divided by 7

⇒ 7³ⁿ + 14n + 21 + 3

⇒ 7(7^{3n - 1} + 2n + 3) + 3

Number = Divisor × Dividend + Remainder

So, the remainder is 3

∴ 7³ⁿ + 14n + 24 when divided by 7 will leave the remainder 3.