Question : The remainder of the term $9 + 9^{2} + \dots + 9^{(2 n + 1)}$ when divided by 6 is:
Option 1: 1
Option 2: 4
Option 3: 2
Option 4: 3

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Question : A positive integer, when divided by 425, gives a remainder of 45. When the same number is divided by 17, the remainder will be:
Option 1: 11
Option 2: 8
Option 3: 9
Option 4: 10

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Answer 1

Correct Answer: 3

Solution : Given, $9 + 9^{2} + \dots + 9^{(2 n + 1)}$ is divided by 6
Consider, $9 + 9^{2} + \dots + 9^{(2 n + 1)}$
Here, for each term in the series, the remainder when divided by 6 is 3.
The sum of the remainder of each term = 3 + 3 + 3 + ............+ up to 2n + 1 terms
2n + 1 is an odd number, so when the sum of an odd number times 3 is divided by 6, the remainder is 3.
Hence, the correct answer is 3.

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Question : The remainder of the term 9+92+…+9(2n+1) when divided by 6 is:Option 1: 1Option 2: 4Option 3: 2Option 4: 3

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Question : The remainder of the term $9 + 9^{2} + \dots + 9^{(2 n + 1)}$ when divided by 6 is:
Option 1: 1
Option 2: 4
Option 3: 2
Option 4: 3