3 added 23 characters in body edited Jan 3 '15 at 8:10 Johannes 4,0321111 silver badges4141 bronze badges Starting with $$1$$, you proceed as follows: Add $$1$$, and multiply the result by $$10$$. This gives you $$20$$. Subtract $$1$$, and multiply the result by $$9$$. This gives you $$171$$. Add $$1$$, and multiply the result by $$8$$. This gives you $$1376$$. Subtract $$1$$, and multiply by $$7$$. This gives you $$9625$$. Etc. How do you get to this result? Look at the last three numbers given. If you take the ratio of the last two values ($$288775/57756$$), you get a result very close to $$5$$. If you take the ratio $$57756/9625$$ You get a result very close to $$6$$. From there on it's just some fiddling... Starting with $$1$$, you proceed as follows: Add $$1$$, and multiply the result by $$10$$. This gives you $$20$$. Subtract $$1$$, and multiply the result by $$9$$. This gives you $$171$$. Add $$1$$, and multiply the result by $$8$$. This gives you $$1376$$. Subtract $$1$$, and multiply by $$7$$. This gives you $$9625$$. Etc. Starting with $$1$$, you proceed as follows: Add $$1$$, and multiply the result by $$10$$. This gives you $$20$$. Subtract $$1$$, and multiply the result by $$9$$. This gives you $$171$$. Add $$1$$, and multiply the result by $$8$$. This gives you $$1376$$. Subtract $$1$$, and multiply by $$7$$. This gives you $$9625$$. Etc. How do you get to this result? Look at the last three numbers given. If you take the ratio of the last two values ($$288775/57756$$), you get a result very close to $$5$$. If you take the ratio $$57756/9625$$ You get a result very close to $$6$$. From there on it's just some fiddling... 2 added 23 characters in body edited Jan 3 '15 at 8:01 Johannes 4,0321111 silver badges4141 bronze badges Starting with $$1$$, you proceed as follows: Add $$1$$, and multiply the result by $$10$$. This gives you $$20$$. Subtract $$1$$, and multiply the result by $$9$$. This gives you $$171$$. Add $$1$$, and multiply the result by $$8$$. This gives you $$1376$$. Subtract $$1$$, and multiply by $$7$$. This gives you $$9625$$. Etc. Starting with $$1$$, you proceed as follows: Add $$1$$, and multiply the result by $$10$$. This gives you $$20$$. Subtract $$1$$, and multiply the result by $$9$$. This gives you $$171$$. Add $$1$$, and multiply the result by $$8$$. This gives you $$1376$$. Subtract $$1$$, and multiply by $$7$$. Etc. Starting with $$1$$, you proceed as follows: Add $$1$$, and multiply the result by $$10$$. This gives you $$20$$. Subtract $$1$$, and multiply the result by $$9$$. This gives you $$171$$. Add $$1$$, and multiply the result by $$8$$. This gives you $$1376$$. Subtract $$1$$, and multiply by $$7$$. This gives you $$9625$$. Etc. 1 answered Jan 3 '15 at 7:55 Johannes 4,0321111 silver badges4141 bronze badges Starting with $$1$$, you proceed as follows: Add $$1$$, and multiply the result by $$10$$. This gives you $$20$$. Subtract $$1$$, and multiply the result by $$9$$. This gives you $$171$$. Add $$1$$, and multiply the result by $$8$$. This gives you $$1376$$. Subtract $$1$$, and multiply by $$7$$. Etc.