Question: How many positive 2-digit numbers are divisible by 6?! 🎬 Set \(a_n = 96\) and solve for \(n\):: Get complete information, detailed analysis, and expert insights. Explore detailed breakdown with verified data and expert analysis. Get comprehensive coverage of all important aspects with latest information. Understand key facts, important details, and complete overview with professional insights. Learn about background, current status, future prospects, and everything you need to know. Discover in-depth analysis, expert commentary, and detailed explanations covering all relevant topics. WARNING: Explicit Content!

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Question: How many positive 2-digit numbers are divisible by 6?

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Solution:

A number is divisible by 6 if it is divisible by both 2 and 3. The smallest 2-digit number is 10 and the largest is 99.

First determine the smallest 2-digit number divisible by 6. Starting from 10 the smallest multiple of 6 is 12.

Next find the largest 2-digit number divisible by 6. From 99 the largest multiple of 6 is 96.

Now find the sequence of 2-digit numbers divisible by 6: 12 18 24 ... 96. This sequence is an arithmetic series where the first term \(a = 12\) and the common difference \(d = 6\).

To find the number of terms use the formula for the \(n\)-th term of an arithmetic sequence:

\[

a_n = a + (n-1) \cdot d

\]

Set \(a_n = 96\) and solve for \(n\):

\[

= 12 + (n-1) \cdot 6