(B) Let the expression be $f(n) = 3^{2n} + 9n + 5$.We can rewrite the expression as $f(n) = 3^{2n} + 9n + 3 + 2$.Now,we can factor out $3$ from the fi

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(B) Let the expression be $f(n) = 3^{2n} + 9n + 5$.We can rewrite the expression as $f(n) = 3^{2n} + 9n + 3 + 2$.Now,we can factor out $3$ from the first three terms:$f(n) = 3(3^{2n-1} + 3n + 1) + 2$.Since $3(3^{2n-1} + 3n + 1)$ is clearly divisible by $3$,the remainder when $f(n)$ is divided by $3$ is $2$.

Competitive Quantitative Aptitude Number system Numbers

Easy

For any integral value of $n$,$3^{2n} + 9n + 5$ when divided by $3$ leaves the remainder:

A
$1$
B
$2$
C
$0$
D
$5$

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Number system

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The product of two natural numbers is $17$. Then the sum of the reciprocals of their squares is

Easy

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$3 \frac{6}{7} + 6 \frac{1}{4} - 5 \frac{1}{3} + 2 \frac{1}{2} = ?$

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In a division sum,the quotient is $120$,the divisor is $456$,and the remainder is $333$. Find the dividend.

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The sum of the first $45$ natural numbers is:

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The sum of three consecutive odd numbers is $20$ more than the first of these numbers. What is the middle number?

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For any integral value of $n$,$3^{2n} + 9n + 5$ when divided by $3$ leaves the remainder:

Similar Questions

The product of two natural numbers is $17$. Then the sum of the reciprocals of their squares is

$3 \frac{6}{7} + 6 \frac{1}{4} - 5 \frac{1}{3} + 2 \frac{1}{2} = ?$

In a division sum,the quotient is $120$,the divisor is $456$,and the remainder is $333$. Find the dividend.

The sum of the first $45$ natural numbers is:

The sum of three consecutive odd numbers is $20$ more than the first of these numbers. What is the middle number?

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