How to install ios 10 on ipad 2 - Tablets & eReaders

Can iPad 3 install iOS 10?
You cannot. A third generation iPad is not compatible with iOS 10. The most recent version it can run is iOS 9.3.5. The iTunes and over the air iOS update servers will only ever allow you to install the most recent compatible version based on the hardware detected by the update system.

According to Apple's official press release, iPad 2 will not run iOS 10.

Go into Settings and select "Software Update." But Apple might not be supporting IOS 10 on an iPad 2.

According to a press release from Apple in 2016, the iPhone 4S, iPad 2, iPad 3, iPad mini, and fifth-generation iPod Touch will not run iOS 10

The easiest way for most people to update iOS 10 to iPhone is over the air, directly on their device. It's fast, efficient and simple to do.

1.Click Settings, then tap on General
2.Tap on Software Update.
3.Tap on Download and Install.
4.Enter your Passcode, if prompted.
5.Tap Agree to the Terms and Conditions. Tap Agree again to confirm.
6.Tap Install Now to begin the update.
http://www.leawo.org/tutorial/how-to-update-ios-9-2-to-iphone.html

If you mean update your iPad to iOS 10, there are two ways for you: update over the air or with iTunes. Here is a detailed post:
How to Install iOS 10 on iPhone iPad

Unfortunately you can only update to 5.1.1 for the ipad1

if you have laptop/desktop computer you can sync the iPad with iTunes and download iOS 8.1.2 there:
Upgrading iPad to iOS 8: Through iTunes 1. Backup your iPad
Open iTunes. Select your iPad in iTunes and click Back Up Now.
2. Restart your iPad and your Computer
3. Download and Install the Update
Go to iTunes -> Select iPad -> Check for Update -> Click Download and Update

Whichever method you choose, the process will take quite some time to work depending on how much free storage you have on your iPad, your internet connection, and how Apple's servers are doing with upgrades. Occasionally, Apple will either not let you download the upgrade or it will fail. For iOS 8, you must have an iPad 3 or newer. This does not work with the original iPad - if something goes wrong, restart your device, and try again.

How to Upgrade to iOS 7 on an iPad or iPad Mini
How to Install iOS 8 When Your Device is Low on Storage

you cannot install iOS 6 because your iPad is too old:
For the iPad first generation (A1219) to update is only possible with connecting the device to iTunes on a computer.
- this model supports only iOS 5 - NO iOS 6/7/8